SSC CGL Tier II 25 Oct 2015 Paper 1

(2) Let the loans taken by A, B and C be Rs. x, Rs. y and Rs. z respectively.
∴ x + y + z = Rs. 7930
S.1. $=\frac{\mathrm{Principal}\times \mathrm{Time}\times \mathrm{Rate}}{100}$
According to the question,
$\mathit{x}+\mathit{x}\times 2\times 5100=\mathit{y}+\frac{\mathit{y}\times 3\times 5}{100}$
$=\mathit{z}+\frac{\mathit{z}\times 4\times 5}{100}$
$\Rightarrow \frac{100\mathit{x}+10\mathit{x}}{100}$
$=\frac{100\mathit{y}+15\mathit{y}}{100}=\frac{100\mathit{z}+20\mathit{z}}{100}$
$\Rightarrow 110\mathit{x}=115\mathit{y}=120\mathit{z}$
$\Rightarrow 22\mathit{x}=23\mathit{y}=24\mathit{z}$
$\Rightarrow \frac{22\mathit{x}}{6072}=\frac{23\mathit{y}}{6072}=\frac{24\mathit{z}}{6072}$
[LCM of 22, 23 and 24 = 6072]
$\Rightarrow \frac{\mathit{x}}{276}=\frac{\mathit{y}}{264}=\frac{\mathit{z}}{253}$
$\therefore \mathit{x}:\mathit{y}:\mathit{z}=276:264:253$
Sum of terms of ratio $=276+264+253=793$
$\therefore$ A's loan $=\frac{276}{793}\times 7930$$=$ Rs. 2760