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?
Answers
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
Step 2 of 2 :
Find the ratio
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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