If a% of a + b% of b = 2% of ab,then what percent of a is b?

Question

A bought a phone from a store and paid \(\frac{1}{6}\) of the price using UPI, \(\frac{1}{3}\) of the price in cash, and the remaining balance a year later. He also paid 10% interest on the remaining balance after one year. What was the original price of the phone?

Answer 1

The provided equation:

\[ \frac{a}{100} \times a + \frac{b}{100} \times b = \frac{2}{100} \times ab \]

Simplified:

\[ \frac{a^2}{100} + \frac{b^2}{100} = \frac{2ab}{100} \]

Multiply both sides by 100:

\[ a^2 + b^2 = 2ab \]

Rearrange:

\[ a^2 - 2ab + b^2 = 0 \]

Factor:

\[ (a - b)^2 = 0 \]

Therefore:

\[ a = b \]

Consequently, \( b \) equals \( a \), meaning \( b \) is 100% of \( a \).

If a% of a + b% of b = 2% of ab,then what percent of a is b?

The Correct Option is D

Solution and Explanation

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