Question

the numerator of a fraction is increased by 20% and denominator is increased by 40% then what percentage of the original fraction is the new fraction​
a. 87.31%
b. 83.4%
c. 90.54%
d. 85.71%

Answer 1

Option (d)

Given :-

♦ The numerator of a fraction is increased by 20% and denominator is increased by 40% .

To find :-

♦ The percentage of the new fraction in the original fraction

Solution :-

Let the numerator of a fraction be X

Let the denominator of the fraction be Y

The original fraction = X/Y

If the numerator is increased by 20% then it will be X + 20% of X

= X + 20% × X

= X + (20/100)×X

= X + (20X/100)

= X + (X/5)

= (5X+X)/5

= 6X/5

If the denominator is increased by 40% then it will be Y + 40% of Y

= Y + 40% × Y

= Y + (40/100)×Y

= Y + (40Y/100)

= Y + (2Y/5)

= (5Y+2Y)/5

= 7Y/5

The new fraction = (6X/5)/(7Y/5)

= (6X/5)×(5/7Y)

= 6X/7Y

= (6/7)(X/Y)

= (6/7) of the Original fraction

Let the percentage of the original fraction be A

=> A =(new fraction/Original fraction)×100

=> A = [(6/7)(X/Y)/(X/Y) ]×100

=> A = (6/7)×100

=> A = (6×100)/7

=> A = 600/7

=> A = 85.71

The percentage = 85.71%

Answer :-

♦ The percentage of the original fraction is the new fraction is 85.71%