Question

On selling a Television for Rs45000 shopkeeper losses 10%. For how much should hesell to gain 5%

Answer 1

Given

• SP of Television= ₹45,000.
• Loss = 10%.
• Gain = 5%.

To Find

• Selling Price.

Solution

In this question, we will first find out the CP from SP and Loss and after that from CP and Gain we can easily find the SP at 5% gain.

Calculating CP

SP = ₹45000.

Loss = 10%.

$\: \: \: \: \: \: \: \: \: \rm{\boxed{\rm{CP = \dfrac{SP \times 100}{100 -Loss\%}}}} \\ \\ \\:\implies\rm{CP = \frac{45000 \times 100}{100+10}} \\ \\ \\:\implies\rm{CP = \frac{4500000}{110}} \\ \\ \\:\implies\rm{CP =₹40909.09.}$

Calculating SP

CP = ₹40909.09.

Gain = 5%.

$\: \: \: \: \: \: \: \: \: \: {\boxed{\rm{CP = \dfrac{SP \times 100}{100+Gain\%}}}} \\ \\ \\: \implies\rm{40909.09 = \frac{SP \times 100}{100 + 5}} \\ \\ \\: \implies\rm{40909.09 = \dfrac{SP \times 100}{105} } \\ \\ \\: \implies\rm{SP\times100 = 40909.09 \times105} \\ \\ \\: \implies\rm{SP = \frac{4295454.45}{100}} \\ \\ \\: \implies\rm{SP = 42954.54}$

Therefore, he should sell ₹42,954.54 to gain 5%.

Used Abbreviations(Short Form)

SP = Selling Price.

CP = Cost Price.

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