Question

Two bicycles were sold for Rs. $3990$ each, gaining $5\%$ on one and losing $5\%$ on the other. The gain or loss $\%$ on the whole transaction is:

• A. neither gain nor loss
• B. $2.5\%$ gain
• C. $2.5\%$ loss
• D. $0.25\%$ loss

Answer 1

The correct option is D $0.25\%$ loss

Let C.P. of each bicycle is Rs. $100$

For $1^{st}$ bicycle

Gain $=5\%$

Then $C.P=\frac{S.P.\times 100}{Gainpercentage}$

$\Rightarrow \frac{3990\times 100}{100+5}$

$\Rightarrow \frac{399000}{105}\Rightarrow$ Rs. $3800$

For $2^{nd}$ bicycle

Loss $=5\%$

Then $C.P=\frac{3990\times 100}{100-5}$

$\Rightarrow \frac{399000}{95}\Rightarrow$ Rs. $4200$

S.P of two bicycle $=3990\times 2=$ Rs. $7980$

C.P. of two bicycle $=3800+4200=$ Rs. $8000$

$\therefore Loss=C.P-S.P.=8000-7980=$ Rs. $20$

Loss $\%=\frac{20}{7980}\times 100$

$\Rightarrow \frac{100}{399}=0.25$ $\%$