# Mohit sold a TV for Rs. 3600, gaining one-sixth of its selling price. What is the gain percent?

(a) 20 %

(b) 22 %

(c) 23%

(d) 25%

Answer

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Hint: Compute the value of gain Mohit made by selling the TV for Rs. 3600. Then use the value of gain to find the cost price. Then we can find the gain percent with the value of gain and the cost price.

Complete step-by-step answer:

Let SP be the selling price of the TV.

Mohit sold the TV for Rs. 3600, hence, we have:

\[SP = 3600..........(1)\]

It is given that the gain is one-sixth of the selling price. Hence, we have:

$\Rightarrow$ \[Gain = \dfrac{1}{6}SP.........(2)\]

Using equation (1) in equation (2) to find the gain, we have:

$\Rightarrow$ \[Gain = \dfrac{1}{6} \times 3600\]

Simplifying the above equation, we determine the gain as:

$\Rightarrow$ \[Gain = 600.........(3)\]

Therefore, the gain is Rs. 600.

Let the cost price of the TV be CP.

We know that the gain is the difference between the selling price and the cost price.

$\Rightarrow$ \[Gain = SP - CP\]

Hence, the formula for finding cost price is as follows:

$\Rightarrow$ \[CP = SP - Gain.........(4)\]

Substituting equation (1) and equation (3) in equation (4), we get:

$\Rightarrow$ \[CP = 3600 - 600\]

$\Rightarrow$ \[CP = 3000..........(5)\]

We know the formula for gain percent, it is as follows:

$\Rightarrow$ \[Gain\% = \dfrac{{Gain}}{{CP}} \times 100\% .........(6)\]

Substituting equation (3) and equation (5) in equation (6), we get:

$\Rightarrow$ \[Gain\% = \dfrac{{600}}{{3000}} \times 100\% \]

Simplifying further, we get:

$\Rightarrow$ \[Gain\% = \dfrac{1}{5} \times 100\% \]

$\Rightarrow$ \[Gain\% = 20\% \]

Hence, the gain percent is 20 %.

Therefore, the correct answer is option (a).

Note: You might consider the gain percent to be one-sixth of 100 % since the gain is given as one-sixth of the selling price but note that gain percent is related with the cost price directly and not the selling price.

Complete step-by-step answer:

Let SP be the selling price of the TV.

Mohit sold the TV for Rs. 3600, hence, we have:

\[SP = 3600..........(1)\]

It is given that the gain is one-sixth of the selling price. Hence, we have:

$\Rightarrow$ \[Gain = \dfrac{1}{6}SP.........(2)\]

Using equation (1) in equation (2) to find the gain, we have:

$\Rightarrow$ \[Gain = \dfrac{1}{6} \times 3600\]

Simplifying the above equation, we determine the gain as:

$\Rightarrow$ \[Gain = 600.........(3)\]

Therefore, the gain is Rs. 600.

Let the cost price of the TV be CP.

We know that the gain is the difference between the selling price and the cost price.

$\Rightarrow$ \[Gain = SP - CP\]

Hence, the formula for finding cost price is as follows:

$\Rightarrow$ \[CP = SP - Gain.........(4)\]

Substituting equation (1) and equation (3) in equation (4), we get:

$\Rightarrow$ \[CP = 3600 - 600\]

$\Rightarrow$ \[CP = 3000..........(5)\]

We know the formula for gain percent, it is as follows:

$\Rightarrow$ \[Gain\% = \dfrac{{Gain}}{{CP}} \times 100\% .........(6)\]

Substituting equation (3) and equation (5) in equation (6), we get:

$\Rightarrow$ \[Gain\% = \dfrac{{600}}{{3000}} \times 100\% \]

Simplifying further, we get:

$\Rightarrow$ \[Gain\% = \dfrac{1}{5} \times 100\% \]

$\Rightarrow$ \[Gain\% = 20\% \]

Hence, the gain percent is 20 %.

Therefore, the correct answer is option (a).

Note: You might consider the gain percent to be one-sixth of 100 % since the gain is given as one-sixth of the selling price but note that gain percent is related with the cost price directly and not the selling price.

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