Concept of “Problem based on ages”–04

Question: Present ages of P and Q are in the ratio 5 : 6 respectively. Seven years hence this ratio becomes 6 : 7 respectively. What is P’s present age in years? [वर्तमान में P तथा Q की उम्र का अनुपात क्रमशः 5 : 6 है; जवकि 7 वर्ष के वाद यह 6  :7 हो जायेगा. P की वर्तमान उम्र क्या है?] [Ans. (a) 35 years] 

(a)  35     (b) 42    (c) 49   (d) can’t be determined (e) None of these 

Solution:

Detailed Explanation:

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

First Method: Given that the present ages of P and Q are in the ratio 5 : 6 respectively; whereas after seven years, this ratio will become 6 : 7 respectively. Here the difference between the corresponding terms is the same.  i. e., 6 – 5 = 7 – 6 = 1 ≡ 7 years (Real difference between the ages of  “present” and “seven year hence” is 7)

         Difference = 1 ≡ 7 years

Present age of P = 5 ≡ 35 years Ans.

Second Method: Let the ages of P and Q, at present, are 5x and 6x. So, their ages, after seven year will be 5x +7 and 6x + 7. But this ratio is given as 6: 7

So, (5x +7)/( 6x + 7) = 6/7

Or, (36–35) x = 7× (7- 6)

Or, x = 7

So, the present age of P = 5x =5×7 = 35 years  

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