Question

If ` 2,600 is divided among the
persons A, B and C in the ratio
1/2 : 1/3 : 1/4 respectively. How
much B gets ?

Answer 1

Given :

Total Amount to be divided : ₹2600

Ratio of division amount : ½:⅓:¼

To find :

The amount received by B.

Solution :

In the question, we are provided with the ratio and the total amount to be divided among A, B and C. To find the amount received by B, we should first take a variable with every part of ratio and then calculate the value of it.

Let the amount distributed to A be ½x.

Let the amount distributed to B be ⅓x.

Let the amount distributed to C be ¼x.

According to the question,

$\sf \dashrightarrow \dfrac{1}{2} : \dfrac{1}{3} : \dfrac{1}{4} = 2600$

$\sf \dashrightarrow \dfrac{1}{2}x + \dfrac{1}{3}x + \dfrac{1}{4}x = 2600$

$\sf \dashrightarrow \dfrac{1x}{2} + \dfrac{1x}{3} + \dfrac{1x}{4} = 2600$

$\sf \dashrightarrow \dfrac{6x + 4x + 3x}{12} = 2600$

$\sf \dashrightarrow \dfrac{13x}{12} = 2600$

$\sf \dashrightarrow 13x = 2600 \times 12$

$\sf \dashrightarrow 13x = 31200$

$\sf \dashrightarrow x = \dfrac{31200}{13}$

$\sf \dashrightarrow x = 2400$

Now, we can find the amount received by each of them.

Amount divided to A :

$\sf \dashrightarrow \dfrac{1}{2}x = \dfrac{1}{2} \times 2400$

$\sf \dashrightarrow \dfrac{2400}{2} = 1200$

Amount distributed to B :

$\sf \dashrightarrow \dfrac{1}{3}x = \dfrac{1}{3} \times 2400$

$\sf \dashrightarrow \dfrac{2400}{3} = 800$

Amount distributed to C :

$\sf \dashrightarrow \dfrac{1}{4}x = \dfrac{1}{4} \times 2400$

$\sf \dashrightarrow \cancel \dfrac{2400}{4} = 600$

Hence, the amount distributed to B is ₹800.