Question

The ratio of the number of pens to the number of erasers at a bookshop was 8:3.
After 290 pens were sold, the ratio became 2: 1. Find the number of erasers at the
bookshop.

Answer 1

Answer:

Number of eraser is 435.

Explanation :

Given ratio :

Pen : eraser = 8 : 3

If 290 pens were sold the ratio becomes 2 : 1

Find the number of erasers.

Let's take the common multiple as ‘a’ units.

So, number of :

• pen ✒ 8a
• eraser ✒3a

290 pens sold

Remaining pens : 8a - 290

Their ratio :

→ pen : eraser

→ (8a - 290) : 3a

According to the question :

→ (8a - 290) : 3a = 2 : 1

→ 8a - 290/3a = 2/1

→ 1(8a - 290) = 2(3a)

→ 8a - 290 = 6a

→ 8a - 6a = 290

→ 2a = 290

→ a = 290/2

→ a = 145

Hence, the number of

• pen : 8a = 8(145) = 1,160.
• eraser : 3a = 3(145) = 435.

-------------------------------

Verification :

Now, we have number of pen is 1,160

And erasers is 3a = 3(145) = 435.

Sell 290 pens

Remains : 1160 - 290 = 870

Form in ratio :

→ pen : eraser

→ 870 : 435

The ratio must be equal to 2 : 1

→ 870 : 435 = 2 : 1

→ 2 : 1 = 2 : 1

L. H. S. = R. H. S.

Hence, verified.

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

Given

• The ratio of the number of pens to the number of erasers at a bookshop was 8:3.

So,

• Let number of pens be 8x

and

• Let number of erasers be 3x.

According to condition,

After 290 pens sold,

• Numbers of pens = 8x - 290

• Number of erasers = 3x

Now,

The ratio of number of pens to number of erasers is 2 : 1.

$\rm :\implies\:\dfrac{8x - 290}{3x} \: =\dfrac{2}{1}$

$\rm :\implies\:8x - 290 \: =6x$

$\rm :\implies\:8x - 6x \: =290$

$\rm :\implies\:2x \: = \: 290$

$\rm :\implies\:x \: = \: 145$

Hence,

$\begin{gathered}\begin{gathered}\bf \: Number \: of \: erasers \: - \begin{cases} &\sf{3x = 3 \times 145 = 435}  \end{cases}\end{gathered}\end{gathered}$