BANKING WIZARD BY PANKAJ GAUTAM

TABLE UPTO 50

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / 20
3 / 6 / 9 / 12 / 15 / 18 / 21 / 24 / 27 / 30
4 / 8 / 12 / 16 / 20 / 24 / 28 / 32 / 36 / 40
5 / 10 / 15 / 20 / 25 / 30 / 35 / 40 / 45 / 50
6 / 12 / 18 / 24 / 30 / 36 / 42 / 48 / 54 / 60
7 / 14 / 21 / 28 / 35 / 42 / 49 / 56 / 63 / 70
8 / 16 / 24 / 32 / 40 / 48 / 56 / 64 / 72 / 80
9 / 18 / 27 / 36 / 45 / 54 / 63 / 72 / 81 / 90
10 / 20 / 30 / 40 / 50 / 60 / 70 / 80 / 90 / 100
11 / 22 / 33 / 44 / 55 / 66 / 77 / 88 / 99 / 110
12 / 24 / 35 / 48 / 60 / 72 / 84 / 96 / 108 / 120
13 / 26 / 39 / 52 / 65 / 78 / 91 / 104 / 117 / 130
14 / 28 / 42 / 56 / 70 / 84 / 98 / 112 / 126 / 140
15 / 30 / 45 / 60 / 75 / 90 / 105 / 120 / 135 / 150
16 / 32 / 48 / 64 / 80 / 96 / 112 / 128 / 144 / 160
17 / 34 / 51 / 68 / 85 / 102 / 119 / 136 / 153 / 170
18 / 36 / 54 / 72 / 90 / 108 / 126 / 144 / 162 / 180
19 / 38 / 57 / 76 / 95 / 114 / 133 / 152 / 171 / 190
20 / 40 / 60 / 80 / 100 / 120 / 140 / 160 / 180 / 200
21 / 42 / 63 / 84 / 105 / 126 / 147 / 168 / 189 / 210
22 / 44 / 66 / 88 / 110 / 132 / 154 / 176 / 198 / 220
23 / 46 / 69 / 92 / 115 / 138 / 161 / 184 / 207 / 230
24 / 48 / 72 / 96 / 120 / 144 / 168 / 192 / 216 / 240
25 / 50 / 75 / 100 / 125 / 150 / 175 / 200 / 225 / 250
26 / 52 / 78 / 104 / 130 / 156 / 182 / 208 / 234 / 260
27 / 54 / 81 / 108 / 135 / 162 / 189 / 216 / 243 / 270
28 / 56 / 84 / 112 / 140 / 168 / 196 / 224 / 352 / 280
29 / 58 / 87 / 116 / 145 / 174 / 203 / 232 / 261 / 290
30 / 60 / 90 / 120 / 150 / 180 / 210 / 240 / 270 / 300
31 / 62 / 93 / 124 / 155 / 186 / 217 / 248 / 279 / 310
32 / 64 / 96 / 128 / 160 / 192 / 224 / 256 / 288 / 320
33 / 66 / 99 / 132 / 165 / 198 / 231 / 264 / 297 / 330
34 / 68 / 102 / 136 / 170 / 204 / 238 / 272 / 306 / 340
35 / 70 / 105 / 140 / 175 / 210 / 245 / 280 / 315 / 350
36 / 72 / 108 / 144 / 180 / 216 / 252 / 288 / 324 / 360
37 / 74 / 111 / 148 / 185 / 222 / 259 / 296 / 333 / 370
38 / 76 / 114 / 152 / 190 / 228 / 266 / 304 / 342 / 380
39 / 78 / 117 / 156 / 195 / 234 / 273 / 312 / 351 / 390
40 / 80 / 120 / 160 / 200 / 240 / 280 / 320 / 360 / 400
41 / 82 / 123 / 164 / 205 / 246 / 287 / 328 / 369 / 410
42 / 84 / 126 / 168 / 210 / 252 / 294 / 336 / 378 / 420
43 / 86 / 129 / 172 / 215 / 258 / 301 / 344 / 387 / 430
44 / 88 / 132 / 176 / 220 / 264 / 308 / 352 / 396 / 440
45 / 90 / 135 / 180 / 225 / 270 / 315 / 360 / 505 / 450
46 / 92 / 138 / 184 / 230 / 276 / 322 / 368 / 414 / 460
47 / 94 / 141 / 188 / 235 / 282 / 329 / 376 / 423 / 470
48 / 96 / 144 / 192 / 240 / 288 / 336 / 384 / 432 / 480
49 / 98 / 147 / 196 / 245 / 294 / 343 / 392 / 441 / 490
50 / 100 / 150 / 200 / 250 / 300 / 350 / 400 / 450 / 500

SQUARE UPTO 50/CUBE UPTO 15/2-5 power upto106-10 power UPTO 5

1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1
2 / 4 / 8 / 16 / 32 / 64 / 128 / 256 / 512 / 1024
3 / 9 / 27 / 81 / 243 / 729 / 2187 / 6561 / 19683 / 59049
4 / 16 / 64 / 256 / 1024 / 4096 / 16384 / 65536 / 262144 / 1048576
5 / 25 / 125 / 625 / 3125 / 15625 / 93750 / 468750 / 2343750 / 11718750
6 / 36 / 216 / 1296 / 7776 / A^0=1
ILLUSTRATION:
3^0=3^1 -3^-1
WE KNOW THAT n^-1=1/n or n^-2=1/n*n
Hence 3^1-3^-1=(1/3)*3=1
Note:A^1/2 or A^.5 would give theroot of A.ie. 25^1/2=5
SUARE OF N AND –N ARE SAME
Example 3square and -3 square are 9.since -×-=+
7 / 49 / 343 / 2401 / 16807 / To find the unit digit only look for the product of unit digit i.e 347×743 look for 3 and 7 only now 3×7=21 unit digit of 21 is 1 therefore unit digit of 347×743=1
8 / 64 / 512 / 4096 / 32768
9 / 81 / 729 / 6561 / 59049
10 / 100 / 1000 / 10000 / 100000
11 / 121 / 1331
12 / 144 / 1728
13 / 169 / 2197
14 / 196 / 2744
15 / 225 / 3375
16 / 256
17 / 289
18 / 324
19 / 361
20 / 400
21 / 441
22 / 484
23 / 529
24 / 576
25 / 625
26 / 676
27 / 729
28 / 784
29 / 841
30 / 900
31 / 961
32 / 1024
33 / 1089
34 / 1156
35 / 1225
36 / 1296
37 / 1369
38 / 1444
39 / 1521
40 / 1600
41 / 1681
42 / 1764
43 / 1849
44 / 1936
45 / 2025
46 / 2116
47 / 2209
48 / 2304
49 / 2401
50 / 2500
cyclicity
0 / 1
1 / 1
2 / 4
3 / 4
4 / 2
5 / 1
6 / 1
7 / 4
8 / 4
9 / 2
Percent / Fraction / Decimals
2.5 / 1/40 / .025
5 / 1/20 / .05
10 / 1/10 / .1
12.5 / 1/8 / .125
15 / 3/20 / .15
16.66 / 1/6 / .166
20 / 1/5 / .2
25 / ¼ / .25
30 / 3/10 / .3
33.33 / 1/3 / .33
35 / 7/20 / .35
37.5 / 3/8 / .375
40 / 2/5 / .4
45 / 9/20 / .45
50 / ½ / .5
55 / 11/20 / .55
60 / 3/5 / .6
65 / 13/20 / .65
66.66 / 2/3 / .66
70 / 7/10 / .7
75 / ¾ / .75
80 / 4/5 / .80
85 / 17/20 / .85
87.5 / 7/8 / .875
90 / 18/20 / .9
95 / 19/20 / .95
100 / 1 / 1
Fraction*100= Percent;
Percent/100=Decimal
100/Percent .Reciprocal(number in the denominator with 1 as numerator)=Fraction
Illustration say 5 percent 5/100=20
Reciprocal=1/20. (Technically speaking reciprocal means flipping the fraction upside down)
Decimal*100=Percent
How it works:
60% of a Number is 90 what would be the80% of a Number. There are two steps to it first to findthe number i.e 100 percent and thereafter its 80%. Normal percentage calculation would be (90×100/60)×80/100.
By Fraction Method (90×5/3)×4/5.
By Decimal method (90×1/.6)×.8/1.
In the first method 100 would cancel out therefore the equation would be (90×80)÷60, In the second method 5 would cancel out therefore the equation would be (90×4)÷3, In the third method 1 and decimal would cancel out and the equation would be (90×8)÷6.
Basically the value which needs to be find out would be kept constant i.e 90 in this case and the other two variables will be dealt with keep 90 constant. Ask yourself the question if 60 percent is 90 80 percent would be more or less it has to be more (this is what should come to your mind)keep your gut feeling in the numerator (my choice on top) and the other variable on the denominator (the thing I didn’t choose will beat the bottom) i.e80 on top 60 bottom and you will get the answer. This is what we call the chain rule (we will discuss in detail in the chain rule questions in the separate chapter) get this concept totally clear tattoo this on your mind.

In 10810 decimal before 1 digit from right is 10 percent i.e 1081 is10 percent of 10810. Decimal before 2 digit is 1 percent i.e 108 is1 percent of 10810.
Illustration : find 35 % of 7740.
Nowdecimal before two digit is 77.4 this is 1 percent multiply by 35 and you will get theanswer.(do normal multiplication 774×35=27090, since there was a decimal before 1 digit place a decimal before 1 digit i.e 2709.0 again since if after decimal there is a 0 and no more integer after 0 then that 0 and decimal has no relevance so the answer would be 2709. In the same question if 30% of 7740 is asked then we know that 774 is 10 %(decimal before 1 digit) therefore 30 % would be 774 ×3=2322.
Concept of reciprocal 1/1/4=1×4/1=4
Illustration when we write 8/2 we find out that how many 2’s are there in the 8 or in other words 8 is constituted of how many 2’s and the answer is 4. Similarly when we write 1/1/4 we want to know that how many ¼ are there in 1 and the answer is 4. (1/4 is 25 paisa 1 rupee is hundred paisa and four 25 paisa makes 1 rupee)
Order Of Operations:
  1. BODMAS=Bracket, of, Division, Multiplication,Addition, Subtraction
  2. PEMDAS=Parentheses,Exponents,Multiplication,Division,Addition,Subtraction.

Reciprocal of a/b =(a/b)-1 , clearly (a/b)-1 =b/a

If there is equal to sign between the numbers then the ratio is inversed. Eg if 4A = 5B then,

A:B =5:4

If 3 variables say 4a=5b=7c then a = b*c (5*7=35) b= a*c (4*7=28) c = a*b (4*5 =20) therefore final ratio would be 35:28:20.

FINDING RATIO
FROM 2 EQUATIONS / A:B / B:C
2:3 / 4:5
1ST STEP / SINCE B IS COMMON HENCE EQUATE IT
HOW? B*B (B OF A:B MULTIPLIED BY B OF B:C
SO B WILL BECOME 12 (4*3 OR 3*4)
2ND STEP / AS SOON AS YOU MULTIPLY THE B’S YOU WILL HAVE TO MULTIPLY THE A’S
AND C’S.
HOW? A* B (OF B:C) AND C * B (OF A:B) SO A WILL BECOME 8 (2*4)
AND C WILL BECOME 15 (3*5)
FINAL RATIO / 8:12:15 (SINCE IT CANNOT BE REDUCED FURTHER)
FRACTION CALCULATIONS
ADDITION / N/D+N/D = (NOF 1ST * D OF 2ND) + (N OF 2ND * D OF IST) /D*D
D OF 1ST * D OF 2ND
EG: ¾ + 4/5 = (3*5)+(4*4)/ (4*5) = 15+16/20= 31/20 = 1+11/20
SUBSTRACTION / N/D-N/D = (NOF 1ST * D OF 2ND) - (N OF 2ND * D OF IST) /D*D
D OF 1ST * D OF 2ND
EG:4/5 - 3/4 = (4*4)-(3*5)/ (4*5) = 16-15/20= 1/20 =
PROOF: WE KNOW THAT 4/5 = 80% AND ¾ = 75%
80% -- 75% = 5% WHICH IN FRACTION IS 1/20 (5/100)
MULTIPLICATION / N/D*N/D = PRODUCT OF NUMERATOR BY PRODUCT OF DENOMINATOR
¾*4/5 = 12/20=3/5 (SINCE 12 AND 20 BOTH ARE MULTIPLE OF 4, HENCE FURTHER REDUCED)
DIVISION / MULTIPLY BY THE RECIPROCAL, 4/5÷2/5 = 4/5 *5/2 = 2
A/B=C/D / HERE NUMERATOR DIVIDES NUMERATOR AND DENOMINATOR DIVIDES DENOMINATOR. N MULTIPLIES WITH D AND VICE VERSA AND THE RESULTANT IS ALWAYS THE VALUE OF 1.

NOTE: ADDITION OF TWO FRACTION WHERE BOTH THE N IS 1 = SUM OF D / PRODUCT OF D; AND SUBTRACTION WOULD BE = DIFFERENCE OF D / PRODUCT OF D.

ADDITION/ SUBSTRACTION OF FRACTION OF MORE THAN TWO VARIABLE THROUGH LCM:

HOW TO DERIVE THE RATIO OF FRACTION?

CASE 1:

Exercise:

  1. Find the approximate value of N when N =[{2(4+5)3×4}/10-23]
  2. 74+(27-24)
  3. (8×9)+7
  4. 2(7-3)+(-4)(5-7)
  5. 2[9-(8÷2)]
  6. 4[-3(3-5)+10-17]
  7. 8(10+5)
  8. (55×12)+(55×88)
  9. a+(b+c-d)
  10. abc+xyc
  11. if x=6. What is the value of 2xy-xy/

------

y

  1. 1/7+5/3
  2. 5/3-1/7
  3. 2/3×6/5
  4. 2/3÷3/4
  5. 6/2/3
  6. 5,2/3+3/8
  7. Reduce 12/60
  8. Convert 9+2/3 to fraction
  9. (4/5/3/5)(1/8/2/3)

¾

  1. .4×.9
  2. 14.3×.232
  3. 12÷.6
  4. 34.26-0.96
  5. 27.3×9.75
  6. 19.6÷3.22
  7. 4/.25/1/50
  8. 3/10×4×.8

.32

  1. Find reciprocal of -8/9, -3.

LAW OF INDICES/SURDS/RADICALS:

The law of Exponents or indices comes from three ideas.

  1. The exponents says how many times to use the number in multiplication.
  2. A negative exponent means divide because the opposite of multiplying is dividing.
  3. A fractional exponent like 1/n means to take the nth root.

LAW of Indices/Exponents

X1=x i.e 21=2

X0=1(already discussed)

X-1=1/x i.e 3-1=1/3

Xm * Xn = X(m+n) i.e 22 * 23 =25

a^m×a^n×a^p=a^(m+n+p)

x^m/x^n=x^(m-n)i.e 5^7/5^4=5^3

(x^m)^n=x^(mn)i.e (4^3)^4=4^12

(xy)^n=x^n×y^n i.e (3×4)^5=3^5×4^5

(x/y)^n=x^n/y^n i.e (7/4)^3=7^3/4^3

X^-n=1/x^ni.e 6^-4=1/6^4

X^(m/n)=n√x^m=(n√x)^m i.e x^(2/3)=3√x^2=(3√x)^2

NOTE: IN THE ABOVE ^ MEANS, POWER FUNCTION

Law of Surds/Radicals

Let a be rational number and n be a positive integer such that a^(1/n)=n√a is called surds of order n.

n√a=a^(1/n)i.e 3√4=3^(1/4)

n√ab=n√a×n√b i.e 4√3×4=4√3×4√4

n√a/b=n√a/n√b

m√n√a=mn√a

(n√a)^n=a

(n√a)^m=n√a^m

Number inside√(root)is called radical.

1.√x√y=√xy eg √12√3=√36=6

2. √x/y=√x/√y e.g √3/16=√3/√16=√3/4

Radicals that are simplified have

  • No fraction left under the radical symbol
  • No perfect power factors in theradical
  • No exponent in the radical greater than index(in n√k n is index and k is radical)
  • No radicals appearing in the denominator of a fraction as answer.
  • To add radicals simplify first if possible and add like radicald
  • To multiply(FOIL)first outside inside later.
  • Rationalizing denominatorwith radical
  • Situation 1(Monomial denominator i.e one term). Multiply both the numeratorand denominator by whatever that makes the denominator an expression that can be simplified so that it no longer contains a radical.

Illustration: 2√7

2/√7×√7/√7(multiplying by √7)=2√7/√49=2√7/7

  • Situation 2 when more than one term in the denominator. Multiply the numerator and denominator by the denominator conjugate. Conjugate is the same expression as denominator but with the opposite sign in the middle, separating the term. Illustration:simplify 2+√5/4-√5?

=2+√5/4-√5×(4+√5/4+√5)=(2+√5)(4+√5)/(4-√5)(4+√5) (foil)=8+2√5+4√5+√25/16+4√5-4√5-√25=8+6√5+5/16-5=13+6√5/11.

  • Situation 3 working with reciprocal you need to rationalize thedenominator. Illustration write the reciprocal of 4-√3=1/4-√3=1/4-√3×(4+√3/4+√3)=1×(4+√3)/(4-√3)×(4+√3) foil

=4+√3/16+4√3×4√3-√9=4+√3/16-3=4+√3/13

Exercise:

  1. Simplify 16(5/4)
  2. Simplify 27-(4/3)
  3. 23×26
  4. (27^-(2/3))^(1/2)
  5. (23)2
  6. 2^(x+5)=2^(x+3)+6
  7. 62×63
  8. 36/32
  9. (43)2
  10. (4y)2
  11. (1/3)2
  12. -33
  13. -3^2
  14. √32
  15. √1/4
  16. Product of two number is-28/27 if one of the no is -4/9 find the other
  17. Find 20 rational number between -5/6 and 5/8
  18. (3/4)-5
  19. 4-6
  20. (2/3)-3
  21. 4-2
  22. (1/6)-2
  23. (2/3)0
  24. 5-3
  25. (1/3)-4
  26. (5/2)-3
  27. (-2)-5
  28. (-3/4)-4
  29. (2/3)3×(2/3)2
  30. 164×43
  31. (4/7)5×(4/7)-3
  32. (√441/961)(both under the root symbol)
  33. Find the square root of 1+(56/169)
  34. Find the value of √243/√363
  35. Find the value of √45×√20
  36. By what least number 3675 be multiplied to get a perfect square? Also find the number whose square is a new number.
  37. By what least number should 6300 be divided to get a perfect square number? Find the number whose square is the new number.
  38. 6c-2/ab-3
  39. (42)0×8-1
  40. Write 4x^3/2x^5y^2 without denominator
  41. Evaluate 4×4^0/2×2^-2
  42. (2x)-3×2x-3

The strange case of 0^0

There are two different arguments for the correct value of 0^0.o^0 could be 1 or possibly 0so some people say it is really indeterminate x^0=1 so0^0=1 but 0^n=0 so 0^0=0 therefore in doubt hence 0^0 is indeterminate.

LCM or the least common multiple is the smallest number which is divided by all the given number. HCF Or the Highest Common Factor is the largest Number which divides all the given Number. There are several ways of finding HCF and LCM simplest of which is the factorization Method. We will discuss this in the classroom presentation.

[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]



PROPERTIES OF NUMBER:

  1. Sum of first n natural number=n(n+1)/2 illustration sum of first 5 natural number =(5×6)/2=15 equation can be further derived as( n square+n)/2=(5 square+5)/2=15. What if asked sum of natural number from 8-13 . first find out 1-13 then 1 -7. The difference of the two would be the answer. Ie (13×14)/2=91 and (7×8)/2=28 91-28=63. Hence sum from 8 to 13 would be =63. 8+9+10+11+12+13=63.
  2. Sum of square OF first n natural number =n(n+1)(2n+1)/6. Illustration sum of square of natural number from 1-7=(7×8×15)/6=140. 1+4+9+16+25+36+49=140.
  3. Sum of cube of first n natural number= (square of last no.+ square of last +1 number)/4. Illustration sum of cube from 1-4= 16×25/4=1=100/ 1+8+27+64=100.
  4. Average of first n natural number(1+lastnumber)/2 illustration average from 1-21=1+21/2=11. Average of any range would be (first number +LAST NUMBER)/2. AVERAGE FROM 20-24=(20+24)/2=22.
  5. Sum till n even number=(n÷2)×{(n÷2)+1} illustration sum till20 even number =(10×11)=110
  6. Sum of n even number =n×(n+1) illustration sum of 20 even number =20×21=420.
  7. Average till n even number=(n÷2)+1 i.e till20= 10+1=11.
  8. Average of n even number=n+1 i.e for 20 =20+1=21
  9. Sum till n odd number=(n+1)^2/4 for 29 it is 30 square /4=900/4=225
  10. Sum of n odd number=n square for 29 it is 29 square=841
  11. Average till n odd number=(n+1)/2 for 21 it is 21+1/2=11
  12. Average of n odd number=n for 21it is=21
  13. (a+b)(a-b)=(a^2-b^2)
  14. (a+b)^2=(a^2+b^2=2ab)
  15. (a-b)^2=(a^2+b^2-2ab)
  16. (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)
  17. (a^3+b^3)=(a+b)(a^2-ab+b^2)
  18. (a^3-b^3)=(a-b)(a^2+ab+b^2)
  19. (a^3+b^3+c^3-3abc)=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)
  20. When a+b+c=0 then a^3+b^3+c^3=3abc.

BINARY NUMBER:

Uses only two digits 0and 1 best way to solve such question is to convert into its integers value and then work it is also advisable to solve such questions with options at times. Trick for Binary conversion start from right hand side with 1 and keep doubling for every left places i.e 1,2,4,8 and so on. Finally ignore the values of all 0 places and add the values of all 1 places. Illustration 110011. Start with right side1 then 2 then 4 then 8 then 16 then 32 you will find that 4 and 8 are at 0 places ignore them, add the other ones i.e 1+2+16+32=51. i.e 110011=51.

Before we move on to question from whatever we have learnt so far in this chapter one pieceof advice Read the questions carefully and observe what the question is asking. (at times look for solution through option and process of elimination i.e the options which could be out rightly rejected. Apply chain rule wherever possible.

QUESTIONS ON NUMBERS AND RATIO PROPORTIONS:

  1. A man engaged a servant on the condition that he would pay him 90 and a turban after service of one year. He served only for 9 months and received the turban and an amount of 65. The price of the turban is:
  2. A boy was provided with 72 chocolates with the condition that for every six chocolate which he would eat he will get an extra chocolate if at the end of the day he had no chocolates left with him then how many chocolates did he eat the entire day?
  3. An army battalion began building wire fence by placing stakes in a row; the stakes were evenly spaced. After placing the first ten stakes the battalion measured the length of the row and found that the row was 27 feet long. They continued the row by placing another 10 stakes and then measured the length of the entire row. How many feet long was the row of stakes the battalion had placed?
  4. After reading 3/5 of his biology homework on Monday. Amit read 1/3 of the remainder on Tuesday. What fraction of his original homework would amit have to read on Wednesday night to complete his biology assignment?
  5. At a college football game 4/5 of the seat in lower deck of the stadium were sold. If ¼ of all the seating in the stadium is located in the lower deck, and if 2/3 of all the seat in the stadium were sold. What fraction of the unsold seat in the stadium were in the lower deck?
  6. On Monday a certain animal shelter housed 55 cats and dogs. By Friday, exactly 1/5 of the cat and ¼ of the dog has to be adopted. No new cats or dogs were brought to the shelter during this period. What is then the greatest possible number of pets that could have been adopted between Monday and Friday?
  7. The Bombay ice cream shoppe sells two flavors vanilla and chocolate. On Friday, the ration of vanilla cone sold to chocolates cone sold was 2:3. If the store had sold 4 more vanilla cone the ratio of vanilla cone sold to chocolate cone sold would have been 3:4. How many vanilla cone did he sold on Friday? (a 32, b 35, c 42, d 48, e 54)
  8. In a certain flower shop, which stocks 4 types of flowers, there are 1/3 as many violets as carnation and ½ as many tulips as violets. If there are equal number of roses and tulips , what percent of flower in the shop are carnations?
  9. Starting at 9 a.m on a certain day, snow began to fall at the rate of 1+1/4 inches every two hours until 3 p.m. if there were already 2+1/4 inches of snow at the ground at 9 a.m. how many inches of snow were on the ground at 3 p.m. ?
  10. Passenger bought ticket at the airline for 1050. Had he bought tickets one day later he would have paid 210 more. How many days before the departure the tickets were purchased? (discount rate 0-6 days 0%, 7-13 days 10%, 14-29 days 25%, 30 days or more 40%).
  11. There are 240 doctors and nurses at the hospital, if the ration of doctors to nurses is 5:7, how many nurses are there in the hospital?
  12. A company profit has doubled for each of the 4 years it has been in existence. If the total profit for those 4 years is 30 million, what were the profits in the first year of operation?
  13. Half the graduating class of a college was accepted by business school. One-third of the class was accepted by law school. 1/5 to both type. What fraction by only law?
  14. A sum of money is divided amongst three persons in the ratio of 4:6:9. If the largest share is 1000 more than the smallest share what is the total sum?
  15. One-third of a two digit number exceeds its one-fourth by 8. What is the sum of the digits of the number?
  16. If a/b=1/2 then the value of a+b/a-b is:
  17. If a/3=b/4=c/7, then the value of a+b+c/c is:
  18. 2/3rd of a number is 10 less than the original number. What is the number?
  19. The sum upto 40 terms of the series 1+2-3, + 1+2-3,------is:
  20. Ifa:b=7:9 and b:c=3:5 then a:b:c is:
  21. A:b=5:9, c:b=2:3, then b gets what percent of the total ?
  22. 3*+ *4 + 7*=152. In this question * should be replaced by what?(a 3, b 4, c 5, d 6, e 7)
  23. A:b=8:15, b:c=5:8, c:d=4:5, then a:d is?
  24. When 75% of a number is added to 75 the result is the no again.what is the no?
  25. Rs. 53 is divided among a,b,c in such a way that a gets rs. 7 more than b and b gets 8 more than c. what is a’s share?
  26. Ram has 6 more than shyam and 9 more than mohan. All the three have 33, how much does ram have?
  27. If teacher wants to line up his students in equal rows and columns. If there are1521 students in total, how many students should be there in the first row?
  28. A third of vinod’s marks in maths exceeds a half of his marks in social studies by 30. If he got 240 marks in the two subjects together. How many marks did he got in social studies? (a 180, b 90, c 30, d 60, e 75).
  29. If a sum is divided between a and b such that 3 times a’s share is the same as 2 times b’s share; what part of the sum is a’s share?
  30. The ratio of number of teacher to the number of students is 1:25. If 36 more students oins, the ratio becomes 1:28. The number of teacher is the school is?
  31. The ratio of number of boys and girls in a school is 3:2. 20% of the boys and 25% of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is?
  32. A boy was asked to multiply a number by 5/7 instead he divided the number by 5/7 and got the answer 24/5 more than what he should have got had he multiplied thenumber by 5/7. Find the number:
  33. A 70 cm long wire is to be cut into two pieces such that one piece will be 2/5 as long as the other. How many centimeters will the shorter piece be?
  34. 37 is divided into two parts. The first part is multiplied by 5 and second part is multiplied 11, then the total is 227. What is the first part?(a 30, b 7, c 37, d 23, e none of these)
  35. If a number of boys in a class is a third more than the number of girls which of the following could represent the strength of the class ? (a 35, b 45,c 60, any of these, e data inadequate, f none of these)
  36. Rs. 210 is divided among a b and c so that if a gets rs. 2 b gets 3 and if b gets 4 c gets 5. What is the share of a?
  37. 6 men earn as much as 8 women, 2 women as much as 3 boys and 4 boys as much as 5 girls. If a girl earns 50 paisa/day. What does a man earn/day?
  38. A gave 1/5th of the money he had tob, b in turn gave 1/3rd of the money he received from a to c. if c received 20, how much money did a had with him initially?(a 240, b 60, c 40, d 20, e none of these)
  39. A trader purchases 210 and 264 liters of oils of two kinds and packages the oils into tins each containing equal quantity of the oils of both kinds. What is the minimum number of tins he has to use?
  40. If 581 is to be divided into three parts such that 4 times the first may be equal to 5 times the second and 7 times the third. What is the first sum?
  41. Find the least number which when successively divided by 9 and 13leaves remainder 7 and 8 respectively?
  42. 351 is divided into three parts in the ratio of ½:1/3:1/4 find the third part?
  43. If the salaries of a and b are in the ratio of 1:2 and the salaries of a and c are in the ratio of 2:3, the salaries of c and b are in the ratio of ?
  44. If the total attendance of the party is 252, which of the following can’t be the ratio of ladies and gents at the party?(a 1:5, b 1:6, c 1:7, d 1:8, e 1:11)
  45. Annual income of a and b are in the ratio of 4:3, whereas their annual expenses are in the ratio of 3:2. If each of them saves 500 at the end of the year, what is the income of b?
  46. An employer reduces the no of his employees in the ratio of 9:8 and increases their salary in the ratio of 14:15. The difference in the amount of bill which was originally 1890 is how much?
  47. 400 are divided amongst 4 men, 5 women and 6 boys such that the share of a man, a woman and a boy are in the ratio of9:8:4. What does a man get?
  48. Find a ratio whose terms differ by 49 and the measure of which is 2/9.
  49. When a earns 20, b earns 30, when b earns 40, c earns 50. When c earns 60 d earns 80, compare the earnings of ,b,c and d.
  50. Ravi earns twice as much in January as in each of the other months. What part of the annual earnings he earns in that month?
  51. 1/3rd of the class wants to go to picnic to patna and ½ to gaya and the others are neutral. If the no f students who are neutral isles by 10 than those who wants to go to gaya. How many students wants to go to patna?(a 20, b 10, c 15, d 5, e none of these)
  52. The no of students in each section of the school is 24. After admitting the new students, 13 new sections were started. Now the total number of section is 16 and there are 21 students in each section. The new students admitted is:
  53. What is the least number which when divided by 2,3,4,5 or 6 leaves a remainder 1 in each case?
  54. A flower man offers f lowers in each temple of he city equal to the number of temples in the city. The total no of flowers offered by him is 1296. Find the total no of temples in the city.
  55. A sum of money is to be divided among p q and r in the ratio of 2:3:5 resectively. If the total share of p and q together is 400 more than q. what is r’s share?
  56. In a factory there are some supervisor and some labor, on their silver jubilee function 2 shirts to each labor and 1 shirt and 1 trouser to each supervisor were distributed. If in all 220 shirts and 20 trousers were distributed. What is the total number of workforce in the factory? (assuming that there is no other designation in the factory)
  57. A sum of money is to be divided among a b and c in the proportion of 2:3:5.