The ratio of ages of Prit and Priti four years ago was 2 : 1. Six

1.	The ratio of ages of Prit and Priti four years ago was 2 : 1. Six years from now the ratio will be 3 : 2. What is the sum of their present ages?1.12 years.2.38 years.3.16 years.4.18 years5. 68 years.
Answer» Correct Answer - Option 2 : 38 years. Given: 4 years ago the ratio of ages, ⇒ Prit: Priti = 2 : 1 6 years from present age, the ratio will be ⇒ Prit: Priti = 3 : 2 Calculation: For 4 years ago, Let the ages of Prit and Priti = 2x : x ∴ In the present the ages will be = 2x + 4 : x + 4 For 6 years from now the ages will be = 2x + 4 + 6 : x + 4 +6 ⇒2x + 10: x + 10 ∴ \(\frac{{2{\rm{x}} + 10}}{{{\rm{x}} + 10}} = {\rm{\;}}\frac{{3}}{{2}}\) ⇒ 4x + 20 = 3x + 30 ⇒ x = 10 The present age = 2x + 4 : x + 4 ∴ Sum of present ages = (2×10 + 4) + (1×10 +4) ⇒ 24 + 14 ⇒ 38yrs

The ratio of ages of Prit and Priti four years ago was 2 : 1. Six years from now the ratio will be 3 : 2. What is the sum of their present ages?1.12 years.2.38 years.3.16 years.4.18 years5. 68 years.

Answer» Correct Answer - Option 2 :

38 years.

Given:

4 years ago the ratio of ages,

⇒ Prit: Priti = 2 : 1

6 years from present age, the ratio will be

⇒ Prit: Priti = 3 : 2

Calculation:

For 4 years ago,

Let the ages of Prit and Priti = 2x : x

∴ In the present the ages will be = 2x + 4 : x + 4

For 6 years from now the ages will be = 2x + 4 + 6 : x + 4 +6

⇒2x + 10: x + 10

∴ \(\frac{{2{\rm{x}} + 10}}{{{\rm{x}} + 10}} = {\rm{\;}}\frac{{3}}{{2}}\)

⇒ 4x + 20 = 3x + 30

⇒ x = 10

The present age = 2x + 4 : x + 4

∴ Sum of present ages = (2×10 + 4) + (1×10 +4)

⇒ 24 + 14

⇒ 38yrs

Discussion

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