Question

A person bought two clocks. The cost price of one of them exceeds by $\frac{1}{4}$ the price of the other. He sold the costlier clock to the dealer at a gain of $10\%$ and the other at a gain of $7.5\%$ and thus got $Rs98$ in all as $SP.$ Find the total cost price of two clocks

• A. $Rs150$
• B. $Rs90$
• C. $Rs120$
• D. $Rs100$

Answer 1

The correct option is B $Rs90$

$1$Clock Let CP of $1$st clock be $x$. Gain$=10\%$

$2$Clock Then, CP of $2$nd clock$=x-\frac{1}{4}x$ $=\frac{3x}{4}$ Gain=$7.5\%$

Total SP=Rs.$98$

Then according to question,

$98=\frac{110}{100}\times x+\frac{107.5}{100}\times \frac{3x}{4}\Rightarrow 98=\frac{11x}{10}+\frac{1075}{1000}\times \frac{3x}{4}\Rightarrow 98=\frac{4400x+3225x}{4000}\Rightarrow x=\frac{98\times 4000}{7625}\Rightarrow x=51.4$

Now, $\frac{3x}{4}=\frac{3\times 51.4}{4}=Rs.38.55$

$\therefore$Total CP=$x+\frac{3x}{4}=Rs.51.4+Rs.38.55$

=Rs.$89.95$

=Rs.$90$(approx.)