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In a family of husband, wife and a daughter, the sum of the husband’s age, twice the wife’s age, and thrice the daughter’s age is 85; while the sum of twice the husband’s age, four times the wife’s age, and six times the daughter’s age is 170. It is also given that the sum of five times the husband’s age, ten times the wife’s age and fifteen times the daughter’s age equals 450. The number of possible solutions, in terms of the ages of the husband, wife and the daughter, to this problem is:








Infinitely many

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Option(A) is correct

Let the age of husband wife and daughter be denoted by $h, w$ and $d$ respectively.

$h+2w+3d=85$ -------- (i)

$2h+4w+6d=170$ -------- (ii)

$5h+10w+15d=450$ -------- (iii)

Multiplying the first equation by 5 we get


but Eq (iii) gives $5h+10w+15d=450$

So No solution possible.

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