Question

At a school swimming event 1/3 of the students were boys . Given that 2/5 of the boys and 3/5 of the girls did not know how to swim . How many students were there altogether if there were 490 swimmers at the event ..?

Answer 1

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✒At a school swimming event 1/3 of the students were boys . Given that 2/5 of the boys and 3/5 of the girls did not know how to swim . How many students were there altogether if there were 490 swimmers at the event ..?

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⏭ Total no. of students were 1050

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✔GIVEN..

✏1/3 of students were boys.

✏2/5 of boys and 3/5 of girls were not swimmers.

✏Total no. of swimmers were 490

✔TO FIND...

✏Total no..of students

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$\large{ \sf{ \star{ \: \: let \: the \: no. \: of \: students \: \: be \: \red{x}}}} \\ \\ : \large{ \sf{ \implies{no. \: of \: boys = \frac{x}{3} }}} \\ \\ : \large{ \sf{ \implies{then \: no. \: of \: girls = \green{ x - \frac{x}{3} = \frac{2x}{3} }}}} \\ \\ \\ \large{ \sf{ \red{ then \: the \: no. \: of \: non \: swimmers...}}} \\ \\ \large{ \sf{ \bullet{ \: \: then \: \frac{2}{5} \times \frac{x}{3} + \frac{3}{5} \times \frac{2x}{3} =x - 490}}} \\ \sf{ \purple{ \underline{because \: 490 \: were \: swimmers..}}} \\ \\ : \large{ \sf{ \implies{ \frac{2x}{15} + \frac{6x}{15} = x - 490}}} \\ \\ : \large{ \sf{ \implies{ \frac{2x + 6x}{15} = x - 490}}} \\ \\ : \large{ \sf{ \implies{ \frac{8x}{15} = x - 490}}} \\ \\ \sf{ \purple{ \underline{cross \: multiplying}}} \\ \\ : \large{ \sf{ \implies{15(x - 490) = 8x}}} \\ \\ : \large{ \sf{ \implies{15x - 490 \times 15 = 8x}}} \\ \\ : \large{ \sf{ \implies{7x = 490 \times 15}}} \\ \\ : \large{ \sf{ \implies{x = \frac{70 \: \: \cancel{490} \times 15}{ \cancel{7}}}}} \\ \\ : \large{ \sf{ \implies{ \green{ \boxed{x = 1050}}}}}$

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$\large{ \bold{ \orange{ \underline{required \: answer \: is \: 1050}}}}$