Present ages of p & q are in the ratio 5:6 respectively. Seven years hence, this ratio becomes 6:7. What is p's present age in years?Rs later the father's age would be four times that of his son. Find the present age of the son?
Answers
Correct Question:
Present ages of p & q are in the ratio 5:6 respectively. Seven years hence, this ratio becomes 6:7. What is p's present age in years?
Given:
p:q = 5:6
___After 7 years___
(p+7):(q+7) = 6:7
To find:
Age of p
Solution:
p/q = 5/6
=> p = 5q/6 ..(1)
(p+7)/(q+7) = 6/7
=> 7(p+7) = 6(q+7)
Put (1):
=> 7(5q/6 + 7) = 6q + 42
=> 7(5q + 42)/6 = 6q + 42
=> 35q + 294 = 36q + 252
=> q = 42
p = 5q/6 = 5 × 42/6 = 5 × 7 = 35
Thus, p is 35 years old.
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Question
Present ages of p & q are in the ratio 5:6 respectively. Seven years hence, this ratio becomes 6:7. What is p's present age in years?
Answer
Present age of p is 35 years.
Explanation
Let the present age of p be 5M years and present age of q be 6M years.
Seven years hence, this ratio becomes 6:7.
Seven years hence,
- Age of p = (5M + 7) years
- Age of q = (6M + 7) years
According to question,
→ (5M + 7)/(6M + 7) = 6/7
Cross-multiply them
→ 7(5M + 7) = 6(6M + 7)
→ 35M + 49 = 36M + 42
→ 49 - 42 = 36M - 35M
→ 7 = M
→ M = 7
Therefore,
Present age of p = 5M = 5(7) = 35 years
Present age of q = 6M = 6(7) = 42 years
Verification
From above calculations we have M = 7
Substitute value of M in (5M + 7)/(6M + 7) = 6/7
→ (5*7 + 7)/(6*7 + 7) = 6/7
→ (35 + 7)/(42 + 7) = 6/7
→ 42/49 = 6/7
→ 6/7 = 6/7