Question

One year ago the ratio between Laxman's and Gopal's salary was $3:4$. The ratio of their individual salaries between last year's and this year's salaries are $4:5$ and $2:3$ respectively. At present the total of their salary is $Rs.4160$. At present, the salary of Laxman, is _______.

• A. $Rs.1040$
• B. $Rs.1600$
• C. $Rs.2560$
• D. $Rs.3120$

Answer 1

The correct option is B $Rs.1600$

Let the salaries of Laxman and Gopal one year before be $L_1\&G_1$ respectively and now be $L_2\&G_2$ respectively.

Therefore, as given:-

$\frac{L_1}{G_1}=\frac{3}{4}⟶{eq}^n\left(i\right)$

$\frac{L_1}{L_2}=\frac{4}{5}⟶{eq}^n\left(ii\right)$

$\frac{G_1}{G_2}=\frac{2}{3}⟶{eq}^n\left(iii\right)$

$L_2+G_2=4160⟶{eq}^n\left(iv\right)$

From ${eq}^n\left(ii\right)\&\left(iii\right)$, we get

$L_1=\frac{4}{5}{L}_2\&G_1=\frac{2}{3}{G}_2$

On putting the value of $L_1\&G_{1}in{eq}^n\left(i\right)$, we get

$\frac{\frac{4}{5}{L}_2}{\frac{2}{3}{G}_2}=\frac{3}{4}$

$\Rightarrow \frac{12L_2}{10G_2}=\frac{3}{4}$

$\Rightarrow \frac{L_2}{G_2}=\frac{5}{8}$

$\Rightarrow G_2=\frac{8}{5}{L}_2⟶{eq}^{n}v$

On solving ${eq}^n\left(iv\right)\&\left(v\right)$, we get

$L_2+\frac{8}{5}{L}_2=4160$

$\Rightarrow \frac{13}{5}{L}_2=4160$

$\Rightarrow L_2=4160\times \frac{5}{13}=1600$

Hence, the salary of Laxman, at present, is Rs.1600