One year ago,the ratio of Ramu's and Somu's a | vedclass

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(D) Let the present ages of Ramu and Somu be $R$ and $S$ respectively.One year ago,the ratio of their ages was $(R-1) : (S-1) = 6 : 7$.This implies $7

Vedclass · Accepted Answer

$36$

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(D) Let the present ages of Ramu and Somu be $R$ and $S$ respectively.One year ago,the ratio of their ages was $(R-1) : (S-1) = 6 : 7$.This implies $7(R-1) = 6(S-1)$,so $7R - 7 = 6S - 6$,which simplifies to $7R - 6S = 1$ (Equation $i$).Four years hence,the ratio of their ages will be $(R+4) : (S+4) = 7 : 8$.This implies $8(R+4) = 7(S+4)$,so $8R + 32 = 7S + 28$,which simplifies to $8R - 7S = -4$ (Equation $ii$).To solve the system of equations:Multiply Equation $(i)$ by $8$: $56R - 48S = 8$ (Equation $iii$).Multiply Equation $(ii)$ by $7$: $56R - 49S = -28$ (Equation $iv$).Subtract Equation $(iv)$ from Equation $(iii)$:$(56R - 48S) - (56R - 49S) = 8 - (-28)$$S = 36$.Therefore,the present age of Somu is $36$ years.

One year ago,the ratio of Ramu's and Somu's ages was $6:7$ respectively. Four years hence,their ratio will become $7:8$. How old (in years) is Somu?

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