Question

The fraction $\dfrac{x}{y}$ is altered by decreasing x by 25 percent and increasing y by 25 percent. The new fraction is what percent less than the original?
A. 35
B. 40
C. 42
D. 45

Answer 1

Hint: Here, we need to find the percentage change in the old fraction when its numerator and denominator are slightly altered.
Percentage change can be calculated by using the formula = $\dfrac{Old \ value - New \ value }{Old \ value} \times 100$.

Complete step-by-step answer:
The given fraction is $\dfrac{x}{y}$.
Since, x is decreased by 25%, thus,
New x = x – 25% of x.
New x = $x-\dfrac{25}{100} \times $
New x = $x-\dfrac{1}{4}\times x$
New x = $x-0.25x=0.75x$
Also, since, y is increased by 25%, thus,
New y = y + 25% of y
New y = $y+\dfrac{25}{100} \times y$
New y = $y+\dfrac{1}{4}\times y$
New y = $y+0.25y=1.25y$
Thus, the new fraction is $\dfrac{New \ x}{New \ y}=\dfrac{0.75x}{1.25y}$.
New Fraction = $\dfrac{75x}{125y}=\dfrac{3x}{5y}$
New Fraction = $0.6 \times \dfrac{x}{y}$
Thus, the new fraction is 0.6 times the original fraction, which implies that the new fraction is 60% of the original fraction.
Hence, the new fraction is (100-60) % = 40% less than the original fraction.
Hence, option B is correct.

Note: In this type of questions involving percentage change in fraction or how much it has increased or decreased, we firstly find the altered fraction according to the given conditions and then compare it with the original fraction to get the required percentage change.