Subject: General Aptitude · Chapter: Profit and Loss · Exam: · Marks: · Difficulty:
A shopkeeper bought three watches $\mathrm{w}_{1}, \mathrm{w}_{2}$ and $\mathrm{w}_{3}$ from a dealer and sold them to three different customers. The ratio of the selling prices of the watches $\mathrm{w}_{1}, \mathrm{w}_{2}$ and $\mathrm{w}_{3}$ was $2: 3: 4$. The shopkeeper gains 30\% and 20\% on the watches $\mathrm{w}_{1}$ and $\mathrm{w}_{2}$ respectively but loses 40\% on the watch $\mathrm{w}_{3}$. What was the shopkeeper's approximate percent gain or loss in the whole transaction?
(a)16\% profit
(b)16\% loss
(c)15\% loss
(d)Data inadequate
Answer
Answer (as printed): B
Explanation
Let the S.P. of watches $w_{1}, w_{2}$ and $w_{3}$ be $₹ 2 x$, ₹ $3 x$ and ₹ $4 x$ respectively. Gain on watch $w_{1}=30 \%$. C.P. of watch $w_{1}=₹\left(\frac{100}{130} \times 2 x\right)=₹ \frac{20 x}{13}$. Gain on watch $w_{2}=20 \%$. C.P. of watch $w_{2}=₹\left(\frac{100}{120} \times 3 x\right)=₹ \frac{5 x}{2}$. Loss on watch $w_{3}=40 \%$. C.P. of watch $w_{3}=₹\left(\frac{100}{60} \times 4 x\right)=₹ \frac{20 x}{3}$. Total C.P. of three watches $=₹\left(\frac{20 x}{13}+\frac{5 x}{2}+\frac{20 x}{3}\right)$ $$=₹\left(\frac{120 x+195 x+520 x}{78}\right)=₹ \frac{835 x}{78} .$$ Total S.P. of three watches $=₹(2 x+3 x+4 x)=9 x$. Loss $=₹\left(\frac{835 x}{78}-9 x\right)=₹ \frac{133 x}{78}$. $$\begin{aligned} \therefore \text { Loss } \% & =\left(\frac{133 x}{78} \times \frac{78}{835 x} \times 100\right) \% \\ & =\left(\frac{2660}{167}\right) \%=15.93 \% \approx 16 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.