Question

A lady has 25 p and 50 p coins in her purse. If in all she has 40 coins totaling Rs. 12.50, find the number of coins of each type she has.

Answer 1

SOLUTION :

First convert Paise into Rupees :
1 Rs = 100 paise
so, 1 paise = 0.01 Rs
and , 25 p = 0.25 Rs
50 p = 0.50 Rs

Let the no of 0.5 Rs coins be ' x'
Let the no .of 0.25 Rs coins be ' y'

By given 1st condition ,
x + y = 40 ...........(1)

By given 2nd condition ,
0.5x + 0.25 y = 12.50 ..............(2)

By elimination method :

Multiply equation (1) by 0.5
0.5 * ( x + y = 40)
0.5x + 0.5y = 20 ...........(3)

Subtract equation (2) and (3) on both sides RHS and LHS .

0.5x + 0.5y = 20.00
-(0.5x + 0.25y = 12.50)

0.5x + 0.50y = 20.00
-0.5x - 0.25y = -12.50
________________
0 + 0.25y = 7.5
y = 7.5/0.25
y = 750 /25
y = 30

Now subsitute the value of , y = 30 in equation (1).

x + 30 = 40
x = 40 - 30
x = 10

hence ,there are 10 coins of 50 paise/0.50 Rs and 30 coins of 25 paise/0.25 Rs