A shopkeeper sold one-fourth of his goods at a loss of 10%. He sold th

1.	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» (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.

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»

(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.