Question

Ahmed, Batuk, and Chand share $\$1000$ in the ratio 8:7:5. Calculate the amount each receives.

Answer 1

Hint: To find the amount Ahmed, Batuk, and Chand receive, the first step is to convert the ratio of the amount each receives into an equation form with the given ratios as “8x”, “5x” and “7x” and find that value. We can substitute this value in the share of each one of them to get the amount received by Ahmed, Batuk, and Chand.

Complete step-by-step solution:
A total amount of $\$1000$is being divided among Ahmed, Batuk, and Chand in the 8:7:5 ratio. Let us have each part of the share to be equal to x, (i.e.) $\$1000$ is being divided into parts of x. Therefore, Ahmed receives “8x” part of the share of $\$1000$, Batuk receives “7x” part of the share of $\$1000$ and Chand receives “5x” part of the share of $\$1000$.
In equation form,
$8x+7x+5x=1000...........(i)$
On adding the values on the left hand side of the equation (i), we get
$20x=1000$
$\Rightarrow x=\dfrac{1000}{20}$
$\therefore x=50$
Now we can obtain the amount received by each of the three people. Ahmed receives “8x” part of the share of $\$1000$. Replacing $x=50$, we get $8x=8\times 50=400$
Batuk receives “7x” part of the share of $\$1000$. Replacing $x=50$, we get $7x=7\times 50=350$
Chand receives “5x” part of the share of $\$1000$. Replacing $x=50$, we get $5x=5\times 50=250$
Hence we find that Ahmed receives $\$400$, Batuk receives $\$350$ and Chand receives $\$250$ as a share of $\$1000$ respectively.

Note: If we add the total amount received by Ahmed, Batuk, and Chand we should get $\$1000$. Note that $\$400+\$350+\$250=\$1000$. This verifies our answer. Do not ever directly multiply a given ratio with the total amount and write the answer, for example, do not multiply 8 by 1000 and write Ahmed’s share as Rs. 8000. This is not correct. We have been given ratios, so we must consider a variable, take ratio as 8x, and then proceed further.