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11. Two numbers are in the ratio of 3 : 1. If sum of these two numbers is 880, find the numbers.
  A.  First Number: 650; Second Number: 210
  B.  First Number: 660; Second Number: 220
  C.  First Number: 640; Second Number: 230
  D.  First Number: 670; Second Number: 220
     
   
View Answer

We use the following short cut method to find the numbers First no. = ax/a+b Second no. = bx/a+b Let a = 3, b = 1 x = 880 ∴ First no. = ax/a+b = 3x880/3+1 = 660 Second no. = bx/a+b = 1 x 880/3+1 = 220

12. A purse contains an equal number of Re 1, 50 paise and 25 paise coins respectively. If the total value is Rs 35, how many coins of each type are there?
  A.  20 coins of each type
  B.  10 coins of each type
  C.  40 coins of each type
  D.  30 coins of each type
     
   
View Answer

We use formula: No. of each type of coins = Amount in Rupees/Value of coins in rupees = 35/(1 + 0.5 + 0.25) = 20 Hence, 20 coins of each type

13. A bag contains Re 1, 50 paise and 25 paise coins whose values are in the ratio of 2 : 3 : 4. If the total number of coins are 480, find the value of each coin.
  A.  Value of Re 1 coin: Rs 10; value of 50 paise coin: Rs 50; Value of 25 paise coin: Rs 80
  B.  Value of Re 1 coin: Rs 20; value of 50 paise coin: Rs 60; Value of 25 paise coin: Rs 50
  C.  Value of Re 1 coin: Rs 30; value of 50 paise coin: Rs 40; Value of 25 paise coin: Rs 20
  D.  Value of Re 1 coin: Rs 40; value of 50 paise coin: Rs 60; Value of 25 paise coin: Rs 80
     
   
View Answer

We use formula: No. of each type of coins = Amount in Rupees/Value of coins in rupees No. of 1 Rupee coin = 2x/1 No. of 50 paise coin = 3x/1/2 No. of 25 paise coin = 4x/1/4 ∴ 2x + 6x + 16x = 480 ∴ x = 20 ∴ Value of 1 rupee coin = 2x = Rs 40 Value of 50 paise coin = 3x = Rs 60 Value of 25 paise coin = 4x = Rs 80

14. The ratio of the number of boys and girls in a school is 2 : 5. If there are 350 students in the school, find the number of girls and boys in the school.
  A.  210 girls; 110 boys
  B.  260 girls; 105 boys
  C.  250 girls; 100 boys
  D.  210 girls; 140 boys
     
   
View Answer

We use the following short cut method to find the numbers First no. = ax/a+b Second no. = bx/a+b Let a = 2, b = 5 x = 350 ∴ Girls = bx/a+b = 5 x 350/2+5 = 250 Boys = ax/a+b = 2x350/2+5 = 100

15. A bag contains Re 1, 50 paise and 25 paise coins in the ratio 5 : 7 : 9. If the total amount in the bag is Rs 430, find the number of coins of each kind.
  A.  Number of Re 1 coin: 100; Number of 50 paise coins:250; Number of 25 paise coins:340
  B.  Number of Re 1 coin: 200; Number of 50 paise coins:280; Number of 25 paise coins:360
  C.  Number of Re 1 coin: 220; Number of 50 paise coins:220; Number of 25 paise coins:320
  D.  Number of Re 1 coin: 250; Number of 50 paise coins:270; Number of 25 paise coins:300
     
   
View Answer

Ratio among the values of the coins = 5/1 : 7/2 : 9/4 = 20 : 14 : 9 Thus the value of one rupee coins = 430 x 20/43 = Rs 200 the value of 50-paise coin = 430 x 14/43 = Rs 140 the value of 25-paise coin = 430 x 9/43 = Rs 90 ∴ the number of one-rupee coins = 200 x 1 = 200 the number of 50-paise coins = 140 x 2 = 280 the number of 25-paise coins = 90 x 4 = 360

16. Raju adds 3 litres of water to 12 litres of milk and another 4 litres of water to 10 litres of milk. What is the ratio of the strengths of milk in the two mixtures?
  A.  30 : 25
  B.  26 : 25
  C.  28 : 25
  D.  24 : 25
     
   
View Answer

To find the strength to milk, we use formula: Strength of milk in the mixture = Quantity of milk/Total Quantity of mixture ∴ Strength of milk in the first mixture = 12 / 12 + 3 = 12/15 Strength of milk in the second mixture = 10 / 10 + 4 = 10/14 ∴ The ratio of their strengths = 12/15 : 10/14 = 12 x 14 : 15 x 10 = 28 :25

17. Two buckets contain equal quantity of mixtures of wine and water in the ratio 5 : 2 and 6 : 1 respectively. Both the mixtures are now mixed thoroughly. find the ratio of wine to water in the new mixture.
  A.  9 : 3
  B.  3 : 11
  C.  15 : 7
  D.  11 : 3
     
   
View Answer

  Milk Water
Vessel I 5/7 2/7
Vessel II 6/7 1/7
Now, both the mixtures are mixed thoroughly. Therefore, the raio of water to milk in the new vessel =(5/7 + 6/7) : (2/7 + 1/7) = 11/7 : 3/7 = 11 : 3

18. Two vessels containing wine and water in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4. The resulting mixture will have water and wine in the ratio of.
  A.  21 : 76
  B.  31 : 74
  C.  33 : 78
  D.  28 : 71
     
   
View Answer

  Milk Water
Vessel I 1/3 2/3
Vessel II 2/7 5/7
From Vessel 1, 1/5 is taken and from Vessel II, 4/5 is taken. Therefore, the ratio of water to milk in the new vessel = (1/3 x 1/5 + 2/7 x 4/5) : (2/3 x 1/5 + 5/7 x 4/5) = (1/15 + 8/35) : (2/15 + 20/35) = 31/105 : 75/105 = 31 : 74 Short cut method: xx1(x2+y2) + yx2(x1+y1) : xy1(x2+y2) + yy2(x1+y1) Here, x1 : y1 = 1 : 2 x2 : y2 = 2 : 5 x = 1 y = 4 Applying values in the given formula we get, = 1 x 1x(2 + 5) + 4 x 2(1+2): 1 x 2(2 + 5) + 4 x 5(1 + 2) = 1 x 7 + 8 x 3 : 2 x 7 + 20 x 3 = 31 : 74

19. Two numbers are in the ratio of 9 : 14. If the larger number is 55 more than the smaller number, find the both numbers.
  A.  Smallest: 99; Larger: 154
  B.  Smallest: 88; Larger: 142
  C.  Smallest: 96; Larger: 134
  D.  Smallest: 96; Larger: 151
     
   
View Answer

Here, a:b = 9:14 x = 55 Applying these values in short cut method: Smaller number = ax/b-a = 9x55/14-9 = 99 Larger number = bx/b-a = 14x55/14-9 = 154 Hence, numbers are 99 and 154

20. The incentive of A, B and C is in the ratio of 2 : 3 : 5. If C's incentive is Rs 1200 more than A's incentive, B's incentive is:
  A.  Rs 1400
  B.  Rs 1300
  C.  Rs 1200
  D.  Rs 1600
     
   
View Answer

Let the salaries of A,BC be 2x, 3x and 5x respectively Now, 5x - 2x = 1200 3x = 1200 x = 400 ∴ B's monthly salary = 3x = 3 x 400 = Rs 1200

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