PROBLEMS ON RATIO

Problem 1 :

Two numbers are in the ratio 2 : 3 and the difference of their squares is 320. The numbers are :

(a)  12, 18

(b)  16, 24

(c)  14, 21

(d)  None of these

Solution :

Problem 2 :

X, Y, Z together starts a business. If X invests 3 times as much as Y invests and Y invests two third of what Z invests, then the ratio of capitals of X, Y, Z is :

(a)  3 : 9 : 2

(b)  6 : 3 : 2

(c)  3 : 6: 2

(d)  6 : 2 : 3

Solution :

Problem 3 :

An alloy is to contain copper and zinc in the ratio 9 : 4. The zinc required to melt with 24 kg of copper is :

(a)  10⅔ kg

(b)  10⅓ kg

(c)  9⅔ kg

(d)  9 kg

Solution :

Problem 4 :

Two numbers are in the ratio 7 : 8. If 3 is added to each of them, their ratio becomes 8 : 9. The numbers are :

(a)  14, 16

(b)  24, 27

(c)  21, 24

(d)  16, 18

Solution :

Problem 5 :

Ratio of earnings of A and B is 4 : 7. If the earnings of A increase by 50% and that of B decrease by 25%, then the new ratio of their earning becomes 8 : 7. What is A’s earning?

(a)  $21,000

(b)  $26,000

(c)  $28,000

(d)  Data Inadequate

Solution :

Problem 6 :

$407 are to be divided among A, B and C so that their shares are in the ratio ¼ : ⅕ : ⅙. The respective shares of A, B, C are :

(a) $165, $132, $110

(b) $165, $110, $132

(c) $132, $110, $165

(d) $110, $132, $165

Solution :

Problem 7 :

The incomes of A and B are in the ratio 3 : 2 and their expenditures in the ratio 5 : 3. If each saves $1,500, then B’s income is :

(a) $6,000

(b) $4,500

(c) $3,000

(d) $7,500

Solution :

Problem 8 :

In what ratio should tea worth $10 per kg be mixed with tea worth $14 per kg, so that the average price of the mixture may be $11 per kg?

(a)  2 : 1

(b)  3 : 1

(c)  3 : 2

(d)  4 : 3

Solution :

Problem 9 :

The ages of two persons are in the ratio 5 : 7. Eighteen years ago their ages were in the ratio of 8 : 13, their present ages (in years) are :

(a)  50, 70

(b)  40, 56

(c)  70, 50

(d)  None of these

Solution :

Problem 10 :

If A, B and C started a business by investing $126,000, $84,000 and $210,000 respectively. If at the end of the year profit is $242,000, then the share of each person is :

(a)  72,000, 48,400, 1,21,000

(b)  72,600, 48,400, 121,000

(c)  72,000, 49,000, 1,21,000

(d)  48,000, 1,21,400, 72,600

Solution :

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