Question

Divide 20 pens among Sheela and Sangeeta in the ratio of 3:2.

Answer 1

Hint: Assume that the number of pens Sheela gets be 3x and the number of pens Sangeeta gets be 2x. Using the fact that the total number of pens is 20 form an equation in x. Solve for x and hence find the number of pens Sheela gets and the number of pens Sangeeta gets.

Complete step-by-step answer:
We have been given that the ratio in which 20 pens are divided among Sheela and Sangeeta is 3:2. So, first of all we will assume a variable x and then we can express the number of pens each has by multiplying x with 3 and 2 respectively.
Let the number of pens Sheela gets be 3x and the number of pens Sangeeta gets be 2x.
Since the total number of pens is 20, we have
$\begin{align}
  & 2x+3x=20 \\
 & \Rightarrow 5x=20 \\
\end{align}$
Dividing both sides by 5, we get
$x=\dfrac{20}{5}=4$
Hence the number of pens Sheela gets is $3x=3\times 4=12$
Hence Sheela gets 12 pens
Similarly, we have
The number of pens Sangeeta gets is $2x=2\times 4=8$
Hence Sangeeta gets 8 pens.
Hence, we should give Sheela 12 pens and Sangeeta 8 pens in order to divide 20 pens among them in the ratio 3:2.

Note: [1] Alternative Solution:
If we divide x in the ratio ${{a}_{1}}:{{a}_{2}}:\cdots :{{a}_{n}}$ then the numbers are
\[{{V}_{1}}=\dfrac{{{a}_{1}}}{\sum\limits_{r=1}^{n}{{{a}_{r}}}}x,{{V}_{2}}=\dfrac{{{a}_{2}}}{\sum\limits_{r=1}^{n}{{{a}_{r}}}}x,\cdots ,{{V}_{n}}=\dfrac{{{a}_{n}}}{\sum\limits_{r=1}^{n}{{{a}_{r}}}}x\]
Hence If we have to divide 20 in the ratio of 3:2, then
${{V}_{1}}=\dfrac{3}{3+2}\times 20=12$ and ${{V}_{2}}=\dfrac{2}{2+3}\times 20=8$, which is the same as obtained above.
Hence, we should give Sheela 12 pens and Sangeeta 8 pens in order to divide 20 pens among them in the ratio 3:2