Question

32 pens need to be divided among Asha and Usha in the ratio of 3:5. Determine the number of pens each of them gets.

Answer 1

Hint: Assume that the number of pens Asha gets be 3x and the number of pens Usha gets be 5x. Using the fact that the total number of pens is 32 form an equation in x. Solve for x and hence find the number of pens Asha gets and the number of pens Usha gets.

Complete step-by-step answer:
Let the number of pens Asha gets be 3x and the number of pens Usha gets be 5x.
Since the total number of pens is 32, we have
$\begin{align}
  & 5x+3x=32 \\
 & \Rightarrow 8x=32 \\
\end{align}$
Dividing both sides by 8, we get
$x=\dfrac{32}{8}=4$
Hence the number of pens Asha gets is $3x=3\times 4=12$
Hence Asha gets 12 pens
Similarly, we have
The number of pens Usha gets is $5x=5\times 4=20$
Hence Usha gets 20 pens.
Hence, we should give Asha 12 pens and Usha 20 pens in order to divide 32 pens among them in the ratio 3:5

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 32 in the ratio of 3:5, then
\[{{V}_{1}}=\dfrac{3}{3+5}\times 32=12\] and ${{V}_{2}}=\dfrac{5}{3+5}\times 32=20$, which is the same as obtained above.
Hence, we should give Asha 12 pens and Usha 20 pens in order to divide 32 pens among them in the ratio 3:5