Aptitude - Ratio and Proportion
11.
If A : B = 1 : 3, B : C = 5 : 7, C : D = 9 : 7, then A : B : C : D = ?
Answer
A : B = 1 : 3 = 5 : 15
B : C = 5 : 7 = 15 : 21
C : D = 9 : 7 = 219 x 9 : 219 x 7
⇒ A : B = 5 : 15, B : C = 15 : 21 and C : D = 21 : 493
A : B : C : D = 5 : 15 : 21 : 493 = 15 : 45 : 63 : 49
Answer :
Option AExplanation :
A : B = 1 : 3 = 5 : 15
B : C = 5 : 7 = 15 : 21
C : D = 9 : 7 = 219 x 9 : 219 x 7
⇒ A : B = 5 : 15, B : C = 15 : 21 and C : D = 21 : 493
A : B : C : D = 5 : 15 : 21 : 493 = 15 : 45 : 63 : 49
12.
The sum of squares of three numbers which are in the ratio 2 : 3 : 4 is 725. What are these numbers ?
Answer
Let the numbers be 2x, 3x and 4x. Then,
4x2 + 9x2 + 16x2 = 725 ⇒ 29x2 = 725 ⇒ x2 = 25 ⇒ x = 5
∴ The numbers are 10, 15, 20
Answer :
Option AExplanation :
Let the numbers be 2x, 3x and 4x. Then,
4x2 + 9x2 + 16x2 = 725 ⇒ 29x2 = 725 ⇒ x2 = 25 ⇒ x = 5
∴ The numbers are 10, 15, 20
13.
If the income of A is 10% more than that of B and the income of B is 20% less than that of C, then the incomes of A, B, C are in the ratio :
Answer
Let C's income be Rs. 100. Then, B's income = Rs. 80
A's income = (110% of Rs. 80) = Rs.
110100 x 80 
= Rs. 88
∴ A : B : C = 88 : 80 : 100 = 22 : 20 : 25
Answer :
Option BExplanation :
Let C's income be Rs. 100. Then, B's income = Rs. 80
A's income = (110% of Rs. 80) = Rs.
110100 x 80 = Rs. 88∴ A : B : C = 88 : 80 : 100 = 22 : 20 : 25
14.
Two numbers are in the ratio of 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The numbers are :
Answer
Let the numbers be 3x and 5x. Then,
3x + 105x + 10 = 57 ⇒ 7(3x + 10) = 5(5x + 10) ⇒ 4x = (70 − 50) = 20
⇒ x = 5
∴ The numbers are (3 x 5) and (5 x 5), i.e. 15 and 25
Answer :
Option DExplanation :
Let the numbers be 3x and 5x. Then,
3x + 105x + 10 = 57 ⇒ 7(3x + 10) = 5(5x + 10) ⇒ 4x = (70 − 50) = 20
⇒ x = 5
∴ The numbers are (3 x 5) and (5 x 5), i.e. 15 and 25
15.
A bag contains Rs. 216 in the form of one-rupee, 50-paise and 25-paise coins in the ratio of 2 : 3 : 4. The number of 50-paise coins is :
Answer
Let the number of one-rupee, 50-p and 25-p coins be 2x, 3x and 4x respectively. Then,
2x + 3x2 + 4x4 = 216 ⇒ 8x + 6x + 4x = 864
⇒ 18x = 864 ⇒ x = 48
Number of 50-p coins = (3 x 48) = 144
Answer :
Option DExplanation :
Let the number of one-rupee, 50-p and 25-p coins be 2x, 3x and 4x respectively. Then,
2x + 3x2 + 4x4 = 216 ⇒ 8x + 6x + 4x = 864
⇒ 18x = 864 ⇒ x = 48
Number of 50-p coins = (3 x 48) = 144
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