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21. An amount of Rs 900 is distributed among A, B and C in the ratio of 4 : 5 : 6. What is the share of B
  A.  Rs 500
  B.  Rs 300
  C.  Rs 400
  D.  Rs 200
     
   
View Answer

short cut method: Share of B = bx/a+b+c a=4 b=5 c=6 x = 900 Putting these values in short cut method: Share of B =

5x900 / 4+5+6
=
5x900 / 15
= Rs 300

22. Two alloys contain Iron and Carbon in the ratio of 3 : 1 and 5 : 3. In what ratio the two alloys should be added together to get a new alloy having Iron and Carbon in the ratio of 2 : 1?
  A.  2 : 1
  B.  3 : 2
  C.  1 : 2
  D.  5 : 3
     
   
View Answer

Short cut method:

ax/(a+b) + cy/c+d / x+y
x 100% gold
3x/4 + 5y/8 / x+y
x 100% silver Here, a = 3 b = 1 c = 5 d = 3 x = 2 y = 1 Applying these values in short cut, we get: =
6x + 5y / 8(x+y)
x 100% -----------Eq (1) Since, Ratio of silver to copper in the mixed alloy is 2:1 ∴ Percentage quantity of silver in the mixed alloy = 2/3 x 100% = 200/3% -----------Eq (2) From the Eq (1) & (2), we get
6x + 5y / 8(x+y)
x 100% =
200 / 3
x 100%
6x + 5y / 8(x+y)
x 100% =
2 / 3
18x + 15y = 16x + 16y or 18x - 16x =16y-15y 2x = y x/y = 1/2 &implies; x:y = 1:2 Hence the two alloys should be mixed in the ratio of 1:2 Suppose the two alloys are mixed in the ratio of x:y Using the short cut method, percentage quantity of silver in the mixed alloy =
3x/(a+b) + cy/c+d / x+y
x 100% gold

23. In a mixture of 70 litres milk and water are in the ratio of 3 : 2. What are the quantities of milk and water in the mixture?
  A.  Milk: 46 litres; Water: 24 litres
  B.  Milk: 24 litres; Water: 46 litres
  C.  Milk: 32 litres; Water: 38 litres
  D.  Milk: 42 litres; Water: 28 litres
     
   
View Answer

Use shortcut: Milk quantity in the mixture = ax/a+b Water quantity in the mixture = bx/a+b x = 70 a = 3 b = 2 Using these values in the short cut, we get Milk quantity in the mixture = ax/a+b = (3x70)/(3+2) = (3x70)/5 = 42 Water quantity in the mixture = bx/a+b = (2x70)/(3+2) = (2x70)/5 = 28

24. If an alloy contains carbon and Iron in the ratio of 12 : 13, what is the percentage quantity of carbon in the alloy?
  A.  48%
  B.  46%
  C.  42%
  D.  49%
     
   
View Answer

Short cut method: Percentage of carbon = a/a+b x 100% Percentage of Iron = b/a+b x 100% a = 12 b = 13 using these values in short cut, we get: Percentage of carbon = a/a+b x 100% = 12/(12+13) x 100% = 12/25 x 100% = 48%

25. The sum of three number is 147. If the ratio between the first and second be 2 : 3 and that between the second and third be 5 : 8, then find the second number.
  A.  41
  B.  49
  C.  45
  D.  43
     
   
View Answer

The question does not give the direct value of second ratio, but we can find the combined ratio all the three numbers by using the formula

2 3  
  5 8
2x5 = 10 3x5 = 15 3x8 = 24
∴ The second number = 147/(10+15+24) x 15 = 147/49 x 15 = 45

26. The ratio of the money with Reenu and Suman is 7 : 15 and that with Suman and Kanti is 7 : 16. If Reenu has Rs 490, how much money does Kanti have?
  A.  Rs 2800
  B.  Rs 2400
  C.  Rs 2200
  D.  Rs 2500
     
   
View Answer

7 15  
  7 16
7x7 = 49 15x7 = 105 15x16 = 240
Hence, the ratio of money with Reenu, Suman and Kanti is 49:105:240 We see that 49≡ Rs 490 ∴ 240 ≡ Rs 2400

27. If A : B = 3 : 4, B : C = 8 : 10 and C : D = 15 : 17. Then find A : B : C : D.
  A.  6 : 12 : 9 : 17
  B.  5 : 17 : 15 : 11
  C.  7 : 12 : 17 : 9
  D.  9 : 12 : 15 : 17
     
   
View Answer

3 4    
  8 10  
    15 17
3x8x15 = 360 4x8x15 = 480 4x10x15 = 600 4x10x17 = 680
Hence, A:B:C:D = 360:480:600:680 = 36:48:60:68 = 9:12:15:17

28. If A : B = 1 : 2, B : C = 3 : 4, C : D = 2 : 3 and D : E = 3 : 4. Then find A : B : C : D : E
  A.  16 : 12 : 8 : 6 : 3
  B.  6 : 3 : 8 : 16 : 12
  C.  3 : 6 : 8 : 12 : 16
  D.  12 : 6 : 8 : 3 : 16
     
   
View Answer

1 2      
  3 4    
    2 3  
      3 4
1x3x2x3 = 18 2x3x2x3 = 36 2x4x2x3 = 48 2x4x3x3 = 72 2x4x3x4 = 96
Hence, A:B:C:D:E = 18:36:48:72:96 = 3:6:8:12:16

29. A boy follows a girl and takes 5 steps for every 6 steps of the girl, but 4 steps of the boy are equal to 5 steps of the girl. Compare the speed of boy and the girl.
  A.  Boy's speed: Girls's speed=25:24
  B.  Boy's speed: Girls's speed=24:25
  C.  Boy's speed: Girls's speed=23:26
  D.  Boy's speed: Girls's speed=21:24
     
   
View Answer

4 steps of boy = 5 steps of girl 1 steps of boy = 5/4 steps of girl ∴ 5 steps of boy = (5x5)/4 steps of girl ∴ the rate of boy: rate of girl = 25/4 : 6 = 25 : 24

30. Amit can do a piece of work in 16 days, Bhim is 60% more efficient than Amit. Find the number of days it takes Bhim to do the same piece of work.
  A.  14 days
  B.  10 days
  C.  12 days
  D.  11 days
     
   
View Answer

A:B
Efficiency 100:160
Days 160:100
8:5
∴ the number of days taken by Bhim = 16/8 x 5 = 10 short cut method:
100 / 100+60
x 16 =
100 / 160
x 16 = 10 days

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