On selling each of the two radios for Rs 5000, a person neither gained

1.	On selling each of the two radios for Rs 5000, a person neither gained nor lost. If he had sold one radio at 25% gain, then at what per cent loss did she sell the radio ?(a) \(16\frac{2}{3}\)%(b) 18\(\frac{2}{9}\)%(c) 25%(d) 26\(\frac{2}{3}\)%
Answer» (a) \(16\frac{2}{3}\)% 1st radio. S.P. = Rs 5000, Gain = 25% \(\therefore\) C.P. = Rs \(\frac{5000\times100}{125}\) = Rs 4000 2nd radio S.P. = Rs 5000, Loss = x% (say) \(\therefore\) C.P. =\(\frac{5000\times100}{100-X}\) Since the person neither gained nor lost, Total C.P. = Total S.P. \(\Rightarrow\) 4000+ \(\frac{500000}{(100-X)}\) = 10000 \(\Rightarrow\) \(\frac{500000}{(100-X)}\) = 6000 \(\Rightarrow\) 500000 = 600000 – 6000x \(\Rightarrow\) 6000 x = 100000 \(\Rightarrow\) x = \(\frac{100}{6}\)% = \(\frac{50}{3}\)% = 16\(\frac{2}{3}\)%

On selling each of the two radios for Rs 5000, a person neither gained nor lost. If he had sold one radio at 25% gain, then at what per cent loss did she sell the radio ?(a) \(16\frac{2}{3}\)%(b) 18\(\frac{2}{9}\)%(c) 25%(d) 26\(\frac{2}{3}\)%

Answer»

(a) \(16\frac{2}{3}\)%

1st radio.

S.P. = Rs 5000, Gain = 25%

\(\therefore\) C.P. = Rs \(\frac{5000\times100}{125}\) = Rs 4000

2nd radio

S.P. = Rs 5000, Loss = x% (say)

\(\therefore\) C.P. =\(\frac{5000\times100}{100-X}\)

Since the person neither gained nor lost, Total C.P. = Total S.P.

\(\Rightarrow\) 4000+ \(\frac{500000}{(100-X)}\) = 10000

\(\Rightarrow\) \(\frac{500000}{(100-X)}\) = 6000

\(\Rightarrow\) 500000 = 600000 – 6000x

\(\Rightarrow\) 6000 x = 100000

\(\Rightarrow\) x = \(\frac{100}{6}\)% = \(\frac{50}{3}\)% = 16\(\frac{2}{3}\)%