Question

Ramesh gains 5% by selling his old scooter for Rs.6720. If he sells it for Rs. 6500, find his gain or loss per cent .​

Answer 1

Given:

• Ramesh gains 5% by selling his old scooter for ₹6720.
• He sells it for ₹6500.

To Find:

• His gain or loss per cent .

Formulas Used:

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

• $\bf Gain\% = \bigg(\dfrac{Gain }{ C.P} \times 100 \bigg)\%$

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Required Solution:

S.P of old scooter = ₹6720

⠀⠀⠀⠀⠀⠀⠀⠀Gain = 5%

Cost price of old scooter:

$\\ \\➟ \: \: \: \sf \: C.P.= \bigg(\dfrac{ S.P. \times 100}{100 \: + \: gain\%} \bigg) \\ \\ ➟ \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: ₹ \: \sf \: \bigg(\dfrac{ 6720 \times 100}{100 \: + \: 5} \bigg) \\ \\➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf ₹ \bigg(\dfrac{ 6720 \times 100}{1 0 5} \bigg) \\ \\➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: { { \underline{ \boxed {\bigstar{ \pink { \bf₹{6400}}}}}}} \: \: \: \: \:$

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New Selling price = ₹6500

⠀⠀⠀⠀⠀⠀⠀⠀Gain = ₹ (6500 – 6400) = ₹100

$➟ \: \: \: \: \: \: \: \: \: \sf Gain \% = \bigg(\dfrac{Gain }{ C.P} \times 100 \bigg)\% \: \: \: \: \: \\ \\ \sf \: ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg(\dfrac{100 }{ 6400} \times 100 \bigg)\% \: \: \: \: \: \\ \\ \sf \: ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg(\dfrac{100 }{ 64 \cancel{00} }\times 1 \cancel{00} \bigg)\% \: \: \: \: \: \\ \\ \sf \: ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dfrac{25}{16} \% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { { \underline{ \boxed {\bigstar{ \pink { \bf{1 \frac{9}{16} \%}}}}}}} \: \: \: \: \: \: \: \: \: \: \: \:$

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⠀Hence, His gain percent is ${ \sf{1 \dfrac{9}{16} \%}}$