Question

divide 104 pencils among three children in the ratio1/2:1/3:1/4​

Answer 1

Given:-

• Total pencils = 104
• Distribute pencils among three children in the ratio= $\frac{1}{2}$:$\frac{1}{3}$:$\frac{1}{4}$

To Find:-

• Divide 104 pencils = ?

Solution:-

Let the distribution of pencils to 1st child be $\frac{x}{2}$

Let the distribution of pencils to 1st child be $\frac{x}{3}$

Let the distribution of pencils to 1st child be $\frac{x}{4}$

According to the question:

$\sf \implies \: \frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 104 \\ \\ \sf \implies \: \frac{6x + 4x + 3x}{12} = 104 \\ \\ \sf \implies \: 13x = 104 \times 12 \\ \\ \sf \implies \: x = \frac{104 \times 12}{13} \\ \\ \sf \implies \: x = 96$

Hence, x is equal to 96.

1. First child will get = $\frac{x}{2}$=$\frac{96}{2}$=48
2. Second child will get = $\frac{x}{3}$=$\frac{96}{3}$=32
3. Third child will get = $\frac{x}{4}$=$\frac{96}{4}$=24