Denominator of first and second fractions is 4 and 9 respectively. The sum of these two fractions is 43/36 and if the numerator of these fractions is reversed, the sum of the two fractions becomes 4/3. Then the first fraction is what percent of the second fraction.

Denominator of first and second fractions is 4 and 9 respectively. The sum of these two fractions is 43/36 and if the numerator of these fractions is reversed, the sum of the two fractions becomes 4/3. Then the first fraction is what percent of the second fraction. Correct Answer 168.75%

Given:

The denominator of the first and second fractions is 4 and 9.

The sum of these two fractions is 43/36.

After interchanging numerator the sum of the two fractions becomes 4/3

Calculation:

The denominator of the first and second fractions is 4 and 9.

Let the first fraction be a/4 and the second fraction be b/9.

The sum of these two fractions = 43/36.

⇒ (a/4) + (b/9) = 43/36

⇒ (9a + 4b)/36 = 43/36

⇒ 9a + 4b = 43      ----(i)

After interchanging numerator of first and second fractions

The fractions will be b/4 and a/9

After interchanging numerator the sum of the two fractions = 4/3

⇒ (b/4) + (a/9) = 4/3

⇒ (9b + 4a)/36 = 4/3

⇒ 4a + 9b = 48      ----(ii)

Now multiply equation (i) by 4 and (ii) by 9, and subtract (i) from (ii)

⇒ 81b – 16b = 432 – 172

⇒ 65b = 260

⇒ b = 4

Now put the value of b in equation (ii)

⇒ 4a + 9 × 4 = 48

⇒ 4a = 48 – 36

⇒ a = 3

So, the first fraction = 3/4 and the second fraction = 4/9

Now to find the first fraction is what percent of the second fraction

⇒ (first fraction/second fraction) × 100

⇒ × 100

⇒ × 100

⇒ (27/16) × 100 = 168.75%