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 90If 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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