42 oranges are distributed among some boys and girls. If each boy gets 3, then each girl gets 6. But if each boy gets 6 and each girl gets 3, it needs 6 more. The number of girls is

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answer is D.

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Detailed Solution

Let number of boys is x and number of girls is y

According to the question,

$3 x + 6 y = 42$ …(1)

$6 x + 3 y = 42 + 6$ …(2)

Multiply eqn (1) by 2 and then, subtracting eqn (2) from eqn (1).

$6 x + 12 y = 84$ ...(3)

$6 x + 3 y = 48$ ...(2)

Subtract eqn (2) and (3)

$\begin{array}{l} 9 = 36 \\ = 4 \end{array}$

Put the value of y in eqn (2)

$\begin{array}{l} 6 x + 3 \times 4 = 48 \\ 6 x = 48 - 12 \\ 6 x = 36 \\ x = 6 \end{array}$

So, number of girls is 4.

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