Question

A farmer bought 100 eggs for Rs 250. He sells 20 of them at a gain of 5%. At what gain % should he sell the remaining eggs so as to gain 20% on the whole ​

Answer 1

GiveN:

• A farmer bought 100 eggs for ₹250. He sells 20 of them at a gain of 5%.

To FinD:

• At what gain % should he sell the remaining eggs so as to gain 20% on the whole.

RequireD SolutioN:

Cost price of 100 eggs = ₹250

Required gain on the whole :

$= \sf \: \: \: \: 20\% \: of \: ₹ \: 250 \\ \\ \sf \: = \: \: ₹ \bigg( \frac{20}{100} \times 250 \bigg) \\ \\ \sf \: = \: \: ₹ \bigg( \frac{2 \cancel{0}}{1 \cancel{00} } \times 25 \cancel{0 }\bigg) \\ \\ = \bf \: \: \: \: ₹ \: 50 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Cost of 1 egg = $\sf \: ₹ \: \dfrac{250}{100} = ₹2.50$

Cost of 20 eggs = ₹(2.50 × 20) = ₹50

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Gain on 20 eggs:

$= \sf \: \: \: \: 5\% \: of \: ₹ \: 50 \\ \\ \sf \: = \: \: ₹ \bigg( \frac{5}{100} \times 50 \bigg) \\ \\ \sf \: = \: \: ₹ \bigg( \frac{5}{\cancel{100} } \times \cancel{50 }\bigg) \\ \\ = \: \: \: \: \: ₹ \: \sf \: \frac{5}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \bf \: \: \: \: ₹ \: 2.50 \: \: \: \: \: \: \: \: \: \: \:$

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Gain on the remaining eggs :

• ⇛ ₹(50 - 2.50) = ₹47.50

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Cost of 80 eggs = ₹(2.50 × 80) = ₹200

Gain% on 80 eggs:

$➟ \: \: \: \sf \: \bigg( \dfrac{Gain \: on \: 80 \: eggs }{C.P. \: of \: 80 \: eggs} \times 100\% \bigg) \\ \\ ➟ \: \: \: \: \: \: \: \sf \: \: \sf \bigg( \frac{47 .50}{200} \times 100 \bigg)\% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➟ \sf \: \: \: \: \: \: \: \: \: \bigg( \frac{47 .50}{2 \cancel{00} } \times 1 \cancel{00} \bigg)\% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➟ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{47.50}{2} \% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: { \underline{ \boxed{ \bf{ \bigstar{ \purple{23.75\%}}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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• Hence, He should sell the remaining eggs at 23.75% gain.