Question

Government of Nepal decided to distribute some amount of money equally among the girls of ABC school. Had there been 5 girls more, each would have received Rs 60 less. Had there been 5 girls less, each would have received Rs 80 more. (1) (ii) Find the number of girls and the sum received by each. Find the total amount provided by the government to the school.​

Answer 1

Answer:

1. 35 girls received 480 each
2. Rs 16800 was provided

Step-by-step explanation:

You want the amount of money, the number of girls, and the value of a share if 5 more girls would have received Rs 60 less, and 5 fewer girls would have received Rs 80 more.

Setup

Let m and g represent the amount of money and the number of girls, respectively. The two given relationships can be written ...

  $\dfrac{m}{g+5}=\dfrac{m}{g}-60\\\\\dfrac{m}{g-5}=\dfrac{m}{g}+80$

Solution

Solving each of these equations for m, we can equate the expressions:

  $\dfrac{-60}{\dfrac{1}{g+5}-\dfrac{1}{g}}=\dfrac{80}{\dfrac{1}{g-5}-\dfrac{1}{g}}\\\\\\3g(g+5)=4g(g-5)\qquad\text{divide by 4, simplify}\\\\35=g\qquad\text{divide by g, add 20-3g}$

Then the value of m is 4 times either of the expressions above:

  $m=16(35)(35 -5) = 480(35) = 16800$

Note that m = 480(35) means each girl received Rs 480.

The number of girls is 35; the sum received by each is Rs 480.

The total amount provided by the government was Rs 16800.