When 40% of the girls left the school assembly, the ratio of the number of boys to girls became 3 to 4. If there were w girls when the assem

Question

When 40% of the girls left the school assembly, the ratio of the number of boys to girls became 3 to 4. If there were w girls when the assembly started, what was the total number of boys and girls when the assembly started?

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    2021-09-06T03:45:17+00:00

    Number of girls at the time of the assembly started = w

    Number of girls left = 40% of w

    =\frac{40}{100}w

    =\frac{2}{5}w

    Remaining girls = w-\frac{2}{5}w

    =\frac{3}{5}w

    Now, the ratio of the number of boys to girls became 3 to 4.

    Let n be the number of boys.

    Then, n:\frac{3}{5} w=3:4

    Or, \frac{n}{3w/5}= \frac{3}{4}

    \frac{5n}{3w}= \frac{3}{4}

    20n = 9w

    or, n = \frac{9}{20} w

    Total number of boys and girls = \frac{9}{20}w+ \frac{3}{5} w

    = \frac{9}{20}w+ \frac{12}{20} w

    = = \frac{21}{20}w

    Hence, the total number of boys and girs is \frac{21}{20} w.

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