Question

In a class, the number of girls, teachers and boys
are in the ratio 3: 1: 4. For a particular party,
donation of each boy, girl and teacher are in the ratio
6:5:10. The difference between the total amount
donated by teachers and that by boys is 560. What
is the total amount donated by girls?​

Answer 1

ANSWER

Given:

• Ratio of number of girls to number of teachers to number of boys = 3 : 1 : 4
• Ratio of donation done by each boy to donation done by each girl to donation done by each teacher = 6 : 5 : 10
• Difference between total amount donated by boys and teachers = Rs 560

To Find:

• Total amount donated by the girls of the class.

Solution:

We are given that,

⇒ Ratio of number of girls to number of teachers to number of boys = 3 : 1 : 4

So, let the number of girls be 3x, teachers be 1x, and boys be 4x.

That is,

⇒ Number of girls = 3x

⇒ Number of teachers = x

⇒ Number of boys = 4x

Now, we are also given that,

⇒ Ratio of donation done by each boy to donation done by each girl to donation done by each teacher = 6 : 5 : 10

So, let the donation done by each boy be 6y, by each girl be 5y and by each teacher be 10y.

That is,

⇒ Amount donated by each boy = 6y

⇒ Amount donated by each girl = 5y

⇒ Amount donated by each teacher = 10y

Now,

⇒ Total Amount donated by boys = (4x) × (6y) = 24xy

⇒ Total Amount donated by girls = (3x) × (5y) = 15xy

⇒ Total Amount donated by teachers = (x) × (10y) = 10xy

Now, we are also given that,

⇒ Difference between total amount donated by boys and teachers = Rs 560

⇒ (Total amount donated by boys) - (Total amount donated by teachers) = 560

So,

⇒ (24xy) - (10xy) = 560

⇒ 24xy - 10xy = 560

⇒ 14xy = 560

⇒ xy = 560/14

Hence,

⇒ xy = 40

Now, we need to find, the total amount donated by girls.

We found that,

⇒ Total Amount donated by girls = 15xy

Substituting value of xy,

⇒ Total Amount donated by girls = 15(40)

⇒ Total Amount donated by girls = Rs 600

Therefore, the total amount donated by the girls for the party is Rs 600.