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

Correct option is C

Given:

$$\frac{a}{b}$$​.
We are asked to find the new fraction when 50% of the numerator and 80% of the denominator are increased.

Solution:
The new numerator = a + 0.5a = 1.5a
The new denominator = b + 0.8b = 1.8b

The new fraction becomes:

$$\frac{1.5a}{1.8b}\\ \ \\= \frac{\frac{1.5a}{1.8b}}{\frac{a}{b}}\\ \ \\= \frac{1.5a}{1.8b} \times \frac{b}{a} \\ \ \\=\frac{1.5}{1.8}\\ \ \\= \frac{15}{18}\\ \ \\= \frac{5}{6}$$ 

Alternate Method: 

Spose a = 100 

b = 100 

Then $$\frac{100+50}{100+80}$$  

​$$=\frac{150}{180}\\ \ \\=\frac{15}{18}\\ \ \\=\frac{5}{6}$$​​

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