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1. Two numbers are in the ratio $1 \frac{1}{2}$ : $2 \frac{2}{3}$ When each of these is increased by 15, they become in the ratio $1 \frac{2}{3}$ : $2 \frac{1}{2}$ . The greater of the numbers is = ?

A. 27

B. 36

C. 48

D. 64

Solution:

\begin{aligned} A : B \\ \frac{3}{2} : \frac{8}{3} \end{aligned}

take L.C.M. of denominator and multiply)

\Rightarrow \frac{3}{2} \times 6 : \frac{8}{3} \times 6 = 9 x : 16 x

After adding 15 in each we get

\begin{aligned} ∴ \frac{9 x + 15}{16 x + 15} = \frac{5}{3} \times \frac{2}{5} \\ \Rightarrow \frac{9 x + 15}{16 x + 15} = \frac{2}{3} (cross multiply) \\ \Rightarrow 27 x + 45 = 32 x + 30 \\ \Rightarrow 5 x = 15 \\ \Rightarrow x = 3 \\ ∴ Smaller number \\ = 9 \times 3 =  27 \\ Greater number \\ =  16 \times 3 =  48 \end{aligned}

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