19 years ago the average age of a woman and her daughter was 47 5 years At present two times of the ...........

Quant (SSC) Problems based on Ages

19 years ago, the average age of a woman and her daughter was 47.5 years. At present, two times of the woman’s age is equal to five times of the daughter’s age. 19 years hence, what will be the age of daughter?

38 years

34 years

57 years

51 years

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Explanation:

19 years ago, let woman’s age = x years and daughter’s age = y years
Then, x + y = 47.5 × 2 = 95 years, -------- (i)
At present, the age of woman = x + 19 years and the age of daughter = y + 19 years
According to the question, 2(x + 19) = 5(y + 19)
2x – 5y = 95 – 38 = 57 ------- (i)
Equation (i) × 5 + (ii)
7x = 475 + 57 = 532
x = 76
19 years ago, daughter’s age = 95 – x = 95 – 76 = 19 years
At present, daughter’s age = 19 + 19 = 38 years,
19 years hence, daughter’s age = 38 + 19 = 57 years