Question

Narendra sells two cookers for 2574 each. On one he gains 10% and on the other he loses 10%
Find his gain or loss per cent in the whole transaction.​

Answer 1

Given:

• Narendra sells two cookers for 2574 each. On one he gains 10% and on the other he loses 10%.

To Find:

• His gain or loss per cent in the whole transaction.

Formulas used:

• $\bf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: + \: gain\% } \bigg)$

• $\bf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: - \: loss\% } \bigg)$

• $\bf \: Loss = \bigg(\dfrac{Loss }{ Cost \: price} \bigg)\times 100\%$

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First Cooker:

S.P. = ₹ 2574 and gain% = 10%

$\therefore \: \: \: \: \: \: \: \: \: \sf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: + \: gain\% } \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2574 \times 100}{100 + 10} \bigg) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= \: ₹ \: \bigg( \dfrac{2574 \times 10 \cancel0}{11 \cancel0} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2574 \times 10}{11} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{ \cancel{2574 0}}{{ \cancel{1 1}}} \bigg) \\ \\ \: \: \: \: \: \: \sf= ₹ { \underline{ \boxed{ \bf{ \bigstar{ \pink{2340}}}}}}$

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Second Cooker:

S.P. = ₹ 2574 and loss% = 10%

$\therefore \: \: \: \: \: \: \: \: \: \sf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: - \: loss\% } \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2574 \times 100}{100 - 10} \bigg) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= \: ₹ \: \bigg( \dfrac{2574 \times 10 \cancel0}{9 \cancel0} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2574 \times 10}{9} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{ \cancel{2574 0}}{{ \cancel{9}}} \bigg) \\ \\ \: \: \: \: \: \: \sf= ₹ { \underline{ \boxed{ \bf{ \bigstar{ \pink{2860}}}}}}$

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Hence, Total cost price of two cookers:

• ₹ (2340 + 2860) = ₹ 5200

⠀

Total selling price of two cookers:

• ₹ (2574 × 2) = ₹ 5148

⠀

Since, C.P. > S.P., There is a loss.

• Loss = ₹ (5200 - 5148) = ₹ 52

⠀So,

$\sf \: \: \: \: \: \: Loss = \bigg(\dfrac{Loss }{ Cost \: price} \bigg)\times 100\% \\ \\ \sf \: Loss = \bigg(\dfrac{52 }{ 5200} \bigg)\times 100\% \\ \\ \sf \: \therefore \: Loss = \bigg(\dfrac{52 }{ 52 \cancel{00} } \bigg)\times 1 \cancel{00}\% = 1\%$

⠀⠀Hence, Loss percent is 1%