Question

If numerator is increased by 16.66% and denominator is decreased by 14.28%, then fraction becomes reciprocal of itself. Find the original fraction.
1. 6/7
2. 7/6
3. 7/5
4. 5/7

Answer 1

Correct Answer - Option 1 : 6/7

Given:

Increased in numerator = 16.66%

Decreased in denominator = 14.28%

Concept used:

16.66% = 1/6

14.28% = 1/7

Calculation:

Let the fraction be x/y

According to the question,

Numerator = x + x × 16.66%

⇒ x + x × (1/6)

⇒ x + x/6

⇒ (6x + x)/6

⇒ 7x/6

Denominator = y - y × 14.28%

⇒ y - y × (1/7)

⇒ y - y/7

⇒ (7y - y)/7

⇒ 6y/7

Again, according to the question,

(7x/6)/(6y/7) = y/x

⇒ (7x/6) × (7/6y)= y/x 

⇒ 49x/36y = y/x

⇒ x²/y² = 36/49

⇒ x/y = 6/7

∴ The original fraction is 6/7.