Mr. Sinha sold two tape recorders for ₹ 990 each, gaining 10% on one and losing 10% on the other. Find his total loss or gain, as percent, on the whole transaction.

Given:

S.P. of tape recorder = ₹ 990

Gain% on one tape recorder = 10%

Loss% on one tape recorder = 10%

Lets take C.P. of tape recorder be ₹ $x$.

As we know,

$\text{Gain\%} = \dfrac{\text{Gain}}{\text{C.P.}} \times 100\\[1em] \Rightarrow10 = \dfrac{\text{Gain}}{x} \times 100\\[1em] \Rightarrow\text{Gain} = \dfrac{10 \times x}{100}\\[1em] \Rightarrow\text{Gain} = \dfrac{x}{10}$

And,

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow\dfrac{x}{10} = 990 - x\\[1em] \Rightarrow\dfrac{x}{10} + x = 990\\[1em] \Rightarrow\dfrac{x}{10} + \dfrac{10x}{10} = 990\\[1em] \Rightarrow\dfrac{(x + 10x)}{10} = 990\\[1em] \Rightarrow\dfrac{11x}{10} = 990\\[1em] \Rightarrow x = \dfrac{990\times10}{11}\\[1em] \Rightarrow x = \dfrac{9,900}{11}\\[1em] \Rightarrow x = 900$

When S.P. is ₹ 990 and gain% is 10%, then C.P. is ₹ 900.

Now, when loss% = 10%

As we know,

$\text{Loss\%} = \dfrac{\text{Loss}}{\text{C.P.}} \times 100\\[1em] \Rightarrow10 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow\text{Loss} = \dfrac{10 \times x}{100}\\[1em] \Rightarrow\text{Loss} = \dfrac{x}{10}$

And,

$\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\dfrac{x}{10} = x - 990\\[1em] \Rightarrow x - \dfrac{x}{10} = 990\\[1em] \Rightarrow\dfrac{10x}{10} - \dfrac{x}{10} = 990\\[1em] \Rightarrow\dfrac{(10x - x)}{10} = 990\\[1em] \Rightarrow\dfrac{9x}{10} = 990\\[1em] \Rightarrow x = \dfrac{990\times10}{9}\\[1em] \Rightarrow x = \dfrac{9,900}{9}\\[1em] \Rightarrow x = 1,100$

When S.P. is ₹ 990 and loss% is 10%, then C.P. is ₹ 1,100.

Total C.P. of both tape recorder = ₹ 900 + ₹ 1,100

= ₹ 2,000

Total S.P. of both tape recorders = ₹ 990 + ₹ 990

= ₹ 1,980

($\because$ S.P. is lesser than C.P., means article is sold at loss.)

$\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\text{Loss} = ₹ 2,000 - ₹ 1,980\\[1em] =₹ 20$

And,

$\text{Loss\%} = \dfrac{\text{Loss}}{\text{C.P.}}\times100\\[1em] = \dfrac{20}{2000}\times100\%\\[1em] = \dfrac{1}{100}\times100\%\\[1em] = \dfrac{1}{\cancel{100}}\times\cancel{100}\%\\[1em] = 1\%$

Hence, the overall loss percent = 1%.