A sum of money was equally distributed among some boys equal had there been two boys more each would have received Rs. 10 less had there been two boys less each would have received Rs.15 more find the number of Boyd and the sum recived by each
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Q- A sum of money was distributed equally in a class of boys. Had there been 10 boys more, each would have received a rupee less. If there had been 15 boys less , each would have received 3 rupees more. Find the sum of money and the number of boys.
Given,
The total money is distributed equally among all boys
Case 1: If there been 10 boys more, each would have received a rupee less
Case 2: If there had been 15 boys less , each would have received 3 rupees more
To FInd,
The amount of money received by each =?
The total number of boys =?
Solution,
Let the total number of boys be x and the amount of money distributed to one boy be y
The total amount of money = xy
Case 1:
(x + 10)(y - 1) = xy
xy + 10y - x -10 = xy
10y - x = 10
x = 10y - 10 ⇒ Equation 1
Case 2:
(x - 15)(y + 3) = xy
xy + 3x - 15y - 45 = xy
3x - 15y - 45 = 0
Putting value of x from equation 1,
3(10y - 10) - 15y - 45 = 0
30y - 30 -15y - 45 = 0
15y - 75 = 0
15y = 75
y = 75 / 15
y = 5
Putting value of y = 5 in equation 1,
x = 10*5 - 10
x = 50 - 10
x = 40
The number of boys = x = 40
The total amount of money = xy = 40 * 5= 200
Hence, the number of boys in the class is 40 and the sum received by each is Rs. 5. The total money distributed is Rs. 200