# A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A .3

B .4

C .5

D .6

Last updated date: 19th Mar 2023

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Answer

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HINT - In order to solve to this problem, we must choose formula of Gain percent $ = {\text{ }}\dfrac{{\left( {{\text{selling price - cost price}}} \right)}}{{{\text{cost price}}}} \times 100{\text{ }}$along with the proper understanding of the unitary method.

Complete step-by-step answer:

It is given that cost price of 6 toffees =Rs.1

So by unitary method

So cost price of 1 toffee will be equal to Rs. \[\dfrac{1}{6}\]

To get gain of 20%

Using formula of Gain percent $ = {\text{ }}\dfrac{{\left( {{\text{selling price - cost price}}} \right)}}{{{\text{cost price}}}} \times 100{\text{ }}$

Selling price of 1 toffee will be equal to

\[20{\text{ = }}\dfrac{{\left( {{\text{selling price - }}\dfrac{1}{6}} \right)}}{{\dfrac{1}{6}}} \times 100\]

On cross multiplication

\[\dfrac{{20}}{{100}}{\text{ }} \times \dfrac{1}{6}{\text{ = (selling price of 1 toffee) - }}\dfrac{1}{6}\]

On further solving

\[ = \dfrac{1}{5}{\text{ }} \times \dfrac{1}{6}{\text{ = (selling price o 1 toffee) - }}\dfrac{1}{6}\]

\[ = \dfrac{1}{5}{\text{ }} \times \dfrac{1}{6}{\text{ + }}\dfrac{1}{6}{\text{ = (selling price of 1 toffee)}}\]

\[ = \dfrac{1}{6}{\text{ }}\left( {{\text{1 + }}\dfrac{1}{5}} \right){\text{ = (selling price of 1 toffee)}}\]

\[{\text{ = (selling price of 1 toffee) = }}\dfrac{1}{6} \times \left( {\dfrac{6}{5}} \right)\]

\[{\text{ = (selling price of 1 toffee) = }}\left( {\dfrac{1}{5}} \right){\text{ }}\] Rs.

$\because $selling price of 1 toffee will be Rs. \[\dfrac{1}{5}\]

By unitary method

$\therefore $selling price of 5 toffees will be Rs. 1

Hence we can say that for gain of 20%, selling price of 5 toffees will be Rs. 1

In other words, he must sell 5 toffees for a rupee to gain 20%.

Hence Option C is correct.

Note-

Whenever we face such type of problems the key concept we have to remember is that always remember how to calculate gain percentage which is stated above, then applying unitary method (which is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value), we can get the required answer.

Complete step-by-step answer:

It is given that cost price of 6 toffees =Rs.1

So by unitary method

So cost price of 1 toffee will be equal to Rs. \[\dfrac{1}{6}\]

To get gain of 20%

Using formula of Gain percent $ = {\text{ }}\dfrac{{\left( {{\text{selling price - cost price}}} \right)}}{{{\text{cost price}}}} \times 100{\text{ }}$

Selling price of 1 toffee will be equal to

\[20{\text{ = }}\dfrac{{\left( {{\text{selling price - }}\dfrac{1}{6}} \right)}}{{\dfrac{1}{6}}} \times 100\]

On cross multiplication

\[\dfrac{{20}}{{100}}{\text{ }} \times \dfrac{1}{6}{\text{ = (selling price of 1 toffee) - }}\dfrac{1}{6}\]

On further solving

\[ = \dfrac{1}{5}{\text{ }} \times \dfrac{1}{6}{\text{ = (selling price o 1 toffee) - }}\dfrac{1}{6}\]

\[ = \dfrac{1}{5}{\text{ }} \times \dfrac{1}{6}{\text{ + }}\dfrac{1}{6}{\text{ = (selling price of 1 toffee)}}\]

\[ = \dfrac{1}{6}{\text{ }}\left( {{\text{1 + }}\dfrac{1}{5}} \right){\text{ = (selling price of 1 toffee)}}\]

\[{\text{ = (selling price of 1 toffee) = }}\dfrac{1}{6} \times \left( {\dfrac{6}{5}} \right)\]

\[{\text{ = (selling price of 1 toffee) = }}\left( {\dfrac{1}{5}} \right){\text{ }}\] Rs.

$\because $selling price of 1 toffee will be Rs. \[\dfrac{1}{5}\]

By unitary method

$\therefore $selling price of 5 toffees will be Rs. 1

Hence we can say that for gain of 20%, selling price of 5 toffees will be Rs. 1

In other words, he must sell 5 toffees for a rupee to gain 20%.

Hence Option C is correct.

Note-

Whenever we face such type of problems the key concept we have to remember is that always remember how to calculate gain percentage which is stated above, then applying unitary method (which is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value), we can get the required answer.

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