Question

Divide $₹3150$ among A, B and C so that the ratio between the A's share and B's share is $2:5$ and the ratio between the B's share and C's share is $4:7$

Answer 1

Step $1:$Finding the $\text{A:B:C}$:

To find $\text{A:B:C}$, we have to make $\text{B}$ equal in both the ratios then combine them.

$$\begin{gathered} \text{A:B=2:5=}\frac{2}{5} \\ \mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numbers}\mathrm{by}4 \\ \frac{2}{5}=\frac{2\times 4}{5\times 4}=\frac{8}{20} \end{gathered}$$ $$\begin{gathered} \text{B:C=4:7=}\frac{4}{7} \\ \mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numbers}\mathrm{by}5 \\ \frac{4}{7}=\frac{4\times 5}{7\times 5}=\frac{20}{35} \end{gathered}$$

Therefore, $\text{A:B:C=8:20:35}$

Step $2:$ Dividing $₹3150$ among A, B and C:

Given, amount $=₹3150$

Let us find the sum of parts of ratio $\text{A:B:C}$ to get the total number of parts,

Total number of parts $=8+20+35=63$.

Noe divide the amount with the total number of parts, to get the amount per part, we get,

$=\frac{₹3150}{63}=₹50$ per part

Hence, A's share $=₹50\times 8=₹400$

B's share $=₹50\times 20=₹1000$

C's share $=₹50\times 35=₹1750$