Question

A boy spends exactly Rs. 81 for buying some pens and pencils. A pen costs Rs. 7 and a pencil costs Rs. 3. If he purchases the maximum possible number of
pens, what would be the ratio of the number of pens to the number of pencils purchased by him?​

Answer 1

Ratio of the number of pens to the number of pencils purchased by the boy = 3 : 2

Given :

• A boy spends exactly Rs. 81 for buying some pens and pencils.

• A pen costs Rs. 7 and a pencil costs Rs. 3.

• The boy purchases the maximum possible number of pens

To find :

The ratio of the number of pens to the number of pencils purchased by the boy

Solution :

Step 1 of 2 :

Form the equation to find the ratio

Let the boy purchases x pens and y pencils

It is given that the boy spends exactly Rs. 81 for buying some pens and pencils.

A pen costs Rs. 7 and a pencil costs Rs. 3.

By the given condition

$\displaystyle \sf{ 7x + 3y = 81 }$

Step 2 of 2 :

Find the ratio

$\displaystyle \sf{ }7x + 3y = 81$

$\displaystyle \sf{ \implies x = \frac{81 - 3y}{7} }$

Now x and y both must be natural number

We know to find the maximum value of x

For y = 1 we have x = 78/7 which is not a natural number

For y = 2 we have x = 75/7 which is not a natural number

For y = 3 we have x = 72/7 which is not a natural number

For y = 4 we have x = 69/7 which is not a natural number

For y = 5 we have x = 66/7 which is not a natural number

For y = 6 we have x = 63/7 = 9 which is a natural number

So the required value x = 9 , y = 6

∴ The boy purchases the maximum 9 pens , when he purchases 6 pencils

Hence the ratio of the number of pens to the number of pencils purchased by the boy

= 9 : 6

= 3 : 2

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