The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present ages of the father isa)35 yearsb)40 yearsc)30 yearsd)25 yearsCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Given information:
- The present age ratio of father and son is 7:2.
- After 10 years, their age ratio will be 9:4.

Let's assume the present age of father and son as 7x and 2x respectively.

After 10 years, their age will be (7x+10) and (2x+10) respectively.

Now, according to the given information, their age ratio after 10 years will be 9:4. Therefore,

(7x+10)/(2x+10) = 9/4

Solving this equation, we get x = 5.

So, the present age of father = 7x = 7*5 = 35 years.

Therefore, option A is the correct answer.

Answer

Let father age be X and son age be Y. Then
X/Y = 7/2
2X = 7Y ..... (1)
After ten years ,
(X+10)/(Y+10) = 9/4
4(X+10) = 9(Y+10)
4X + 40 = 9Y + 90
4X = 9Y + 50
2×2X = 9Y + 50

putting the value to 2X by equation 1

2×7Y = 9Y + 50
14Y = 9Y + 50
5Y = 50
Y = 10
Son age is 10 years .

putting the value of Y in equation 1

2X = 7Y
X = 7/2Y
X = 7/2×10
X = 70/2
X = 35
Father age is 35.

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