If we increase 50% of numerator and 80% of denominator of a fraction, then what fraction of the original will be the new fraction?

Correct option is B

Given:

The numerator is increased by 50% and the denominator is increased by 80%,

Concept Used

Let the original fraction be \frac{N}{D} , where N is the numerator and D is the denominator.

Solution:

Calculate the new numerator and denominator after increasing them by 50% and 80%, respectively.

The new numerator will be:
​$$N_{\text{new}} = N + 0.5N = 1.5N$$​​

The new denominator will be:
​$$D_{\text{new}} = D + 0.8D = 1.8D$$​​

The new fraction becomes:
​$$\frac{N_{\text{new}}}{D_{\text{new}}} = \frac{1.5N}{1.8D}\\\ \\\frac{1.5N}{1.8D} = \frac{1.5}{1.8} \times \frac{N}{D}$$​​

Since $$\frac{1.5}{1.8} = \frac{5}{6}$$​ , we can rewrite the new fraction as:
​$$\frac{5}{6} \times \frac{N}{D}$$​​

The new fraction is $$\frac{5}{6}$$​ of the original fraction.