Last year there were 610 boys in a school. The number decreased by 20 percent this year. How many girls are there in the school if the number of girls is 175 percent of the total number of boys in the school this year?

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 same problem can be solved using fractions instead of decimals, which avoids any rounding along the way.

A 20% decrease means boys this year are $\dfrac{4}{5}$ of last year's count: boys this year $= \dfrac{4}{5} \times 610 = 488$.

Girls are 175% of this year's boys, and $175\% = \dfrac{7}{4}$, so girls $= \dfrac{7}{4} \times 488$.

$\dfrac{7 \times 488}{4} = \dfrac{3416}{4} = 854$.

So there are 854 girls in the school, matching option A.

\[\boxed{854}\]

Answer 2

The same problem can be solved using fractions instead of decimals, which avoids any rounding along the way.

A 20% decrease means boys this year are $\dfrac{4}{5}$ of last year's count: boys this year $= \dfrac{4}{5} \times 610 = 488$.

Girls are 175% of this year's boys, and $175\% = \dfrac{7}{4}$, so girls $= \dfrac{7}{4} \times 488$.

$\dfrac{7 \times 488}{4} = \dfrac{3416}{4} = 854$.

So there are 854 girls in the school, matching option A.

\[\boxed{854}\]

Last year there were 610 boys in a school. The number decreased by 20 percent this year. How many girls are there in the school if the number of girls is 175 percent of the total number of boys in the school this year?

Show Hint

The Correct Option is A

Solution and Explanation

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