A sum of rs. 64 is made up of 80 coins which are either 100 paise or 50 paise coins. How many coins are of 50 paise?
Answers
Given : A sum of rs. 64 is made up of 80 coins which are either 100 paise or 50 paise coins.
To find : The number of coins of 50 paise .
Solution ;
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of coins of 50 paise)
Let, the number of coins of 50 paise = x
And, the number of coins of 100 paise = y
Total number of coins :
= x+y
According to the data mentioned in the question,
x+y = 80
50 × (x+y) = 50 × 80 [Multiplying both sides with 50]
50x + 50y = 4000 ...(i)
Sum of money by 50 paise coins :
= Number of 50 paise coins × 50 paise
= (x × 50) paise
= 50x paise
Sum of money by 100 paise coins :
= Number of 100 paise coins × 100 paise
= (y × 100) paise
= 100y paise
Total sum of money :
= Sum of money by 50 paise coins + Sum of money by 100 paise coins
= (50x + 100y) paise
Now, as per the data given in the question -
Total sum of money :
= Rs. 64
= (64 × 100) paise [As, 1 rupee = 100 paise]
= 6400 paise
So,
50x + 100y = 6400 ...(ii)
By subtracting (i) from (ii), we get :
ㅤ50x + 100y = 6400
(-) 50x + 50y = 4000
ㅤ- - ㅤㅤㅤ-
_________________
ㅤㅤㅤㅤㅤ50y = 2400
ㅤㅤㅤㅤㅤy = 2400/50
ㅤㅤㅤㅤㅤy = 48
Now, putting the value of y in equation (i) :
50x + (50 × 48) = 4000
50x + 2400 = 4000
50x = 4000 - 2400
50x = 1600
x = 1600/50
x = 32
So, the number of coins of 50 paise = x = 32
(This will be considered as the final result.)
Hence, the number of coins of 50 paise is 32