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Mathematics

A man sold his bicycle for ₹ 405 losing one-tenth of its cost price. Find:

(i) its cost price;

(ii) the loss percent.

Profit, Loss & Discount

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Answer

(i) Given:

S.P. of the bicycle = ₹ 405

Loss = one-tenth of its C.P.

Let the C.P. be ₹ xx.

Loss = 110×x\dfrac{1}{10} \times x

= x10\dfrac{x}{10}

As we know,

Loss = C.P. - S.P.x10=x405xx10=40510x10x10=405(10xx)10=4059x10=405x=405×109x=40509x=450\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\dfrac{x}{10} = x - 405\\[1em] \Rightarrow x - \dfrac{x}{10} = 405\\[1em] \Rightarrow \dfrac{10x}{10} - \dfrac{x}{10} = 405\\[1em] \Rightarrow \dfrac{(10x - x)}{10} = 405\\[1em] \Rightarrow \dfrac{9x}{10} = 405\\[1em] \Rightarrow x = \dfrac{405 \times 10}{9} \\[1em] \Rightarrow x = \dfrac{4050}{9} \\[1em] \Rightarrow x = 450

Hence, the cost price = ₹ 450.

(ii) Loss = one-tenth of the C.P.

= 110×450\dfrac{1}{10} \times 450

= 45010\dfrac{450}{10}

= 4545

Loss%=LossC.P.×100%=45450×100%=110×100%=10%\text{Loss\%} = \dfrac{\text{Loss}}{\text{C.P.}} \times 100\%\\[1em] = \dfrac{45}{450} \times 100\%\\[1em] = \dfrac{1}{10} \times 100\%\\[1em] = 10\%

Hence, the loss percent = 10%.

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