Question

Divide Rs $760$ among $A,B$ and $C$ such that A gets $\dfrac{5}{6}$ of what $B$ gets and the ratio between the shares of $B$ and $C$ is $3:4$.

Answer 1

Hint:As we know that the above given question is a word problem. A problem is a mathematical question written as one sentence or more describing a real life scenario where that problem needs to be solved by the way of mathematical calculation. We can solve the given problem by applying the method of mathematical equations and then solve it.

Complete step by step answer:
We need to first understand the requirement of the question which is the shares of each member. Let us assume that the amount of $B$ is $x$, now from the question we have $A$ gets $\dfrac{5}{6}$ of what $B$ gets. So we can write the amount of $A = \dfrac{5}{6}x$.

Another statement we have is that the ratio between the shares of $B$ and $C$ is $3:4\,or\,\dfrac{3}{4}$. It can be written as $\dfrac{B}{C} = \dfrac{3}{4}$, we can put the value of B in this, so we have $\dfrac{x}{C} = \dfrac{3}{4}$, therefore the amount of C $ = \dfrac{{4x}}{3}$.

Now according to the question total of $A + B + C = 360$. By putting the values back in the equation we can write $\dfrac{{5x}}{6} + x + \dfrac{{4x}}{3} = 760$.
Now we will add and solve for $x$,
$\dfrac{{5x + 6x + 8x}}{6} = 760 \\
\Rightarrow \dfrac{{19x}}{6} = 760$
By isolating the term $x$ we have,
$x = \dfrac{{760 \times 6}}{{19}} = 240$.
So the amount of $B$ is $x = 240$.
We can now calculate the amount of $A$ i.e. $\dfrac{5}{6} \times 240 = 200$.
Similarly the amount of $C$ is $\dfrac{{4 \times 240}}{3} = 320\,Rs$.

Hence the amount of A is $Rs\,200,B = Rs\,240$ and the amount of C is $Rs\,320$.

Note:We should always be careful what the question is asking. We can also cross verify our answer, the question says that the ratio of $B$ and $C$ is $3:4$. We can put the values and check if we get the same ratio. So we have $\dfrac{B}{C} = \dfrac{{240}}{{320}} = \dfrac{3}{4}$. Based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation or by unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.