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Question

Divide 282 into two parts such that the eighth part of the first and the fifth part of the second are in the ratio 4 : 3 are 192 and 90
If true then enter $$1$$ and if false then enter $$0$$


Solution

Let 282 be divided into parts, $$ a $$ and $$ 282 - a $$
Given, eighth part of the first and the fifth part of the second are in the ratio $$ 4 : 3 $$
=> $$ \displaystyle \frac {\dfrac {a}{8}}{\dfrac {282-a}{5}} = \frac {4}{3} $$
=> $$ \displaystyle \frac {5a}{2256 -8a} = \frac {4}{3} $$
Cross-multiplying, $$ 3 \times 5a = 4 \times (2256-8a) $$
$$ 15a = 9024 - 32a $$
$$ 47a  = 9024 $$
$$a = 192 $$
and $$ 282 - 192 = 90 $$
Thus the required parts of $$ 282 $$ are $$ 192, 90 $$

Mathematics

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