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The present age ratio of the mother to the daughter is 7 : 2. After 12 years, their ages will be in the ratio of 9 : 4. What is the current age of the
Question

The present age ratio of the mother to the daughter is 7 : 2. After 12 years, their ages will be in the ratio of 9 : 4. What is the current age of the mother?

A.

48 years

B.

52 years

C.

42 years

D.

38 years

Correct option is C

Given:
The present age ratio of the mother to the daughter is 7:2.
After 12 years, their ages will be in the ratio of 9:4.
Solution:
Let the present age of the mother be 7x and the present age of the daughter be 2x.
According to question

7x+122x+12=944(7x+12)=9(2x+12)28x+48=18x+10828x18x=1084810x=60x=6010=6\frac{7x + 12}{2x + 12} = \frac{9}{4}\\4(7x + 12) = 9(2x + 12)\\28x + 48 = 18x + 108\\28x - 18x = 108 - 48\\10x = 60\\x = \frac{60}{10} = 6\\ 

Current Age of mother = 7x = 7 ×6=42\times 6 = 42  years​

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