Question

# Divide 20 pens between Sheela and Sangeeta in the ratio 3:2.

Hint: First of all consider the pens that Sheela and Sangeeta have as 3x and 2x respectively. Add them and equate it to the total number of pens to get the value of x. Substitute the value of x in 3x and 2x to get the number of pens each one of them has.

Here, we have to divide 20 pens between Sheela and Sangeeta in the ratio 3:2.
Let us consider that Sheela has 3x pens. Let us also consider that Sangeeta has 2x pens.
Now we know that the total pens are 20. So, this means that,
(Number of pens that Sheela has) + (Number of pens that Sangeeta has) = 20
By substituting the number of pens that Sheela has as 3x and number of pens that Sangeeta has as 2x in the above equation, we get,
3x + 2x = 20
By simplifying the above equation, we get,
$\Rightarrow$ 5x = 20
By dividing 5 on both sides of the above equation, we get,
$\Rightarrow$ $\dfrac{5x}{5}=\dfrac{20}{5}$
Therefore, we get x = 4.
Now, we know that the number of pens owned by Sheela = 3x.
By substituting the value of x = 4, we get,
Number of pens owned by Sheela = 3 x 4 = 12 pens.
Now, we also know that the number of pens owned by Sangeeta = 2x.
By substituting the value of x = 4, we get,
Number of pens owned by Sangeeta = 2 x 4 = 8 pens.
Hence, Sheela has 12 pens and Sangeeta has 8 pens.

Note: Here, we can also find the number of pens owned by Sheela and Sangeeta directly by using the formula. If Sheela’s pens and Sangeeta’s pens are in the ratio m:n and total pens are T, then, Number of pens that Sheela has $=\left( \dfrac{m}{m+n} \right).T$ And Number of pens that Sangeeta has $=\left( \dfrac{n}{m+n} \right).T$ Hence, we know that m:n = 3:2, that is m = 3 and n = 2. Also T = 20. So, we get, Number of pens that Sheela has $=\dfrac{\left( 3 \right)}{\left( 3+2 \right)}.20=\dfrac{3}{5}.20=12\text{ pens}$ Number of pens that Sangeeta has $=\dfrac{\left( 2 \right)}{\left( 3+2 \right)}.20=\dfrac{2}{5}.20=8\text{ pens}$