Question

If the numerator of a fraction be increased by 15% and it's denominator be diminished by 8%, the value of the fraction is 15/16 .find the original fraction.

Answer 1

Answer:

★Original fraction = 3 / 4★

Step-by-step explanation:

Given:

• Numerator of a fraction is increased by 15%
• Denominator is decreased by 8%
• Value of fraction is 15/16

To Find:

• Original fraction

Solution: Let the numerator be n and denominator be d . Then, the fraction will be n/d

Now, According to the question

→n is increased by 15%

$\small\implies{\sf }$ n + 15n /100

$\small\implies{\sf }$ n = 23n / 20 ............( Numerator)

→d is decreased by 8%

$\small\implies{\sf }$ d – 8d / 100

$\small\implies{\sf }$ d = 23d/25.............( Denominator)

†Therefore ,

→ 23n/20 ÷ 23d/25 = 15/16

→5n / 4d = 15 / 16

→n / d = 15 / 16 x 4 / 5 ....( Cross Multiply)

Hence, n / d = 3 / 4

Numerator= n = 3

Denominator = d = 4