Question

A box contains pencils, sketch pens and ink pens in the ratio 5:8:3. If the number of sketch pens is 12 more than the number of pencils, find the number of ink pens in the box.

Answer 1

Hint: Consider the ratio in x, that is, 5x:8x:3x. Now, the number of pencils, sketch pens and ink pens are 5x, 8x, and 3x respectively. We are given that the number of sketch pens is 12 more than the number of pencils. In mathematical form, we can express it as $5x+12=8x$. Now, solve this equation and find the value of the unknown variable x. To find the number of ink pens, put the value of x in 3x.

Complete step-by-step answer:
Let us assume that the ratio is x.
Number of pencils = 5x .
Number of sketch pens = 8x .
Number of ink pens = 3x .
According to the question, the number of sketch pens is 12 more than the number of pencils.
Number of sketch pens = 12+ Number of pencil
\[\begin{align}
  & \Rightarrow 8x=5x+12 \\
 & \Rightarrow 3x=12 \\
 & \Rightarrow x=4 \\
\end{align}\]
Now,
Number of pencils = 5(4) =20.
Number of sketch pens = 8(4) = 32 .
Number of ink pens = 3(4) = 12 .
Hence, the number of ink pens is 12.

Note: In this question, we have to find the number of ink pens and it is given that the number of sketch pens is 12 more than the number of pencils. In mathematical form, one may write it as
Number of sketch pens + 12 = Number of pencil …………….(1)
This is wrong. The number of sketch pens is 12 more than the number of pencils. So, we have to add 12 in the number of pencils to make it equal to the number of sketch pens.