Question

Divide $₹6240$ among $\mathrm{A},\mathrm{B}$ and$\mathrm{C}$, in such a way that their shares are in the ratio$\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$.

Answer 1

Step $1:$ Finding the simplest form of $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ :

To convert $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ in the simplest form, multiply each term by the LCM of their denominators.

Since LCM of $2,3$ and $4$ is $12$

Therefore multiply each fraction by$12$, and we get,

$\frac{1}{2}:\frac{1}{3}:\frac{1}{4}=\frac{1}{2}\times 12:\frac{1}{3}\times 12:\frac{1}{4}\times 12=6:4:3$

Hence, the simplest form of $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ is $6:4:3$

Therefore, $\text{A:B:C=6:4:3}$

Step $2:$ Dividing $₹6240$ among $\mathrm{A},\mathrm{B}$ and$\mathrm{C}$ in the ratio $6:4:3$:

Here, amount $=₹6240$

First, do the sum of parts of the ratio $\text{A:B:C}$ to get the total number of parts,

Total number of parts $=6+4+3=13$

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

$=\frac{₹6240}{13}=₹480$ per part

Hence,$\mathrm{A}\text{'}s$ share $=₹480\times 6=₹2880$

$\mathrm{B}\text{'}s$ share $=₹480\times 4=₹1920$

$\mathrm{C}\text{'}s$ share $=₹480\times 3=₹1440$