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Present age of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. Wat is X’s present age?
- a)35
- b)42
- c)49
- d)Cannot be determined
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Present age of X and Y are in the ratio 5:6 respectively. Seven years ...
Let
X present age is 5a---(1)
Y present age is 6a
After 7 years
5a+7/6a+7=6/7
cross multiply
So
7(5a+7)=6(6a+7)
35a+49=36a+42
a=7--(2)
substitute (2) in (1)
X present age is 5(7)= 35
X present age is 5a---(1)
Y present age is 6a
After 7 years
5a+7/6a+7=6/7
cross multiply
So
7(5a+7)=6(6a+7)
35a+49=36a+42
a=7--(2)
substitute (2) in (1)
X present age is 5(7)= 35
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Present age of X and Y are in the ratio 5:6 respectively. Seven years ...
Let the present ages of X and Y be 5k and 6k years, respectively. Seven years later, their ages will be (5k + 7) and (6k + 7). According to the problem, the ratio of their ages after seven years is 6:7. Therefore, (5k + 7)/(6k + 7) = 6/7. Cross-multiplying gives: 7(5k + 7) = 6(6k + 7). Expanding both sides: 35k + 49 = 36k + 42. Subtracting 35k from both sides: 49 = k + 42. Thus, k = 7. Therefore, X’s present age is 5k = 5 × 7 = 35 years.
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