Question

a sum of 2700 is to be given in the form of 63 prizes if the prices of either rupees hundred or rupees 25 find the number of prices of its types​

Answer 1

Let, the number of prize of ₹ 100 be, 'x' and of ₹ 25 be, 'y'

According to the given condition,

x+y = 63 ----------(1)

⇒ x = 63-y ------(2)

By the given condition,

(x*100)+(y*25) = 2700

⇒ 100x+25y = 2700

⇒ 25(4x+y)= 2700

⇒ 4x + y = 2700/25

⇒ 4x + y = 108 ---------(3)

Subtracting equation (2) from equation (3)

4x + y = 108

 x + y =    63

(-)   (-)      (-)

_____________________

 3x       =   45

3x = 45

⇒ x = 45 /3

⇒ x = 15

Putting the value of 'x' in equation (2)

x = 63-y

⇒ 15 = 63-y

⇒ 15+y = 63

⇒ y = 63-15

⇒ y = 48

∴ The number of prizes of ₹ 100 is 15 and the number of prizes of ₹25 is 48.