PROBLEMS BASED ON AGES – 01

Question: One year ago the ratio between Samir’s and Ashok’s age was 4: 3. One year hence the ratio of their ages will be 5 : 4. What is the sum of their present ages in years?  (एक साल पहले समीर और अशोक की उम्रों का अनुपात 4 : 3 था. आज से एक साल बाद  समीर और अशोक की उम्रों का अनुपात 5 : 4 हो जाता है. उनकी वर्तमान उम्रों का योग बताइए.)   

(a) 15 yrs  (b) 13 yrs  (c) 20 yrs  (d) 16 yrs   (e) none of these

Ans. (d) 16 yrs

Solution:

Detailed explanation: First Method: When the differences between the terms of the ratios are the same, then this difference can be taken as equivalent to the real difference.

i. e., 5 – 4 = 4 – 3 = 1 ≡ 2 years (difference between the ages of one year ago and one year hence is 2)

Sum of the ages one year ago = 4 + 3 = 7 ≡ 14 years (as 1 ≡ 2 years)

So, the sum of the ages, at present = (14 + 2) = 16 years  

Or,

Sum of the ages one year hence = 5 + 4 = 9 ≡ 18 years (as 1 ≡ 2 years)

So, the sum of the ages, at present = (18 - 2) = 16 years

Second Method: Let the ages of Samir and Ashok, one year ago are 4x and 3x. So, their present ages, one year hence will be 4x +2 and 3x + 2. But this ratio is given as 5 : 4

 

 So, (16 – 15) x = 2 × (5 - 4); therefore, x = 2 years

Sum of the ages one year ago = 4x + 3x = 7x = 7 × 2 = 14 years

So, the sum of the ages, at present = (14 + 2) = 16 years