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.

Answer 1

Hint: Assume the given numbers to be $x$ and $282-x$ and then equate the given ratio with the assumed ratio which can be formed by following the given conditions that is $\dfrac{x}{282-x}=\dfrac{4}{3}$ and solving for x.

Complete step-by-step answer:
Let the two parts in which 282 is divided by $x$ and $282-x$. According to the given condition, the eighth part of the first i.e $\dfrac{x}{8}$ , and fifth part of the second that is $\dfrac{282-x}{5}$ are in the ratio $4:3\ $. Equating this two ratios we get the following relation :
$$\dfrac{\dfrac{x}{8}}{\dfrac{282-x}{5}}=\dfrac{4}{3}$$
Simplifying and cross multiplying we get,
$$\dfrac{3x}{8}=\dfrac{4\left(282-x\right)}{5}$$
Cross multiplying again and working out the parenthesis we obtain the following linear equation,
$$47x=32\times 282$$
We observe that $282=47\times 6$ which gives us the answer as,
$$x=32\times 6=192$$
The other part is $282-x=282-192=90$ . Thus the two parts are $192$ and $90$ and the given statement is true.

Note : These problems require a basic knowledge of ratio and proportion with familiarity of linear equations. We always need to find a way to form an equation with the given conditions and unknowns that we need to find.