Question

A shopkeeper sold one-fourth of his goods at a loss of 10%. He sold the remaining at a higher per cent of profit to get  12\(\frac{1}{2}\)% profit on the whole transaction. The higher profit per cent is

(a) 17\(\frac{1}{2}\)%

(b) 33\(\frac{1}{3}\)%

(c) 22\(\frac{1}{2}\)%

(d) 20%

Answer 1

(d) 20%

Let C.P. = Rs c

\(\therefore\) C.P. of \(\frac{1}{4}th\) of the goods = \(\frac{\frac{c}{4}\times90}{100}\) = Rs \(\frac{9c}{40}\)

C.P of \(\frac{3}{4}th\) of the goods = Rs \(\frac{3c}{4}\)

Let profit on this remaining part = P%. Then,

S.P. of \(\frac{3}{4}th\) of the goods = \(\frac{\frac{3c}{4}\times(100+P)}{100}\)

= \(\frac{3c}{400}\)(100+P)

Profit on the whole transaction = 12.5%

\(\therefore\) S.P. of the whole = Rs \(\frac{c\times112.5}{100}\)

\(\therefore\) \(\frac{9c}{40}\) + \(\frac{3c}{4}\) + \(\frac{3c\times P}{400}\) = \(\frac{112.5c}{100}\)

\(\Rightarrow\) \(\frac{90+300+3p}{400}\) = \(\frac{112.5}{100}\)

\(\Rightarrow\) \(\frac{390+3p}{4}\) = 112.5  \(\Rightarrow\) 390 + 3P = 450

\(\Rightarrow\) 3P = 60  \(\Rightarrow\) P = 20.