Question

A box had some pens in it. When the pens were distributed equally to 18 children, none remained but while distributing to 19 children, 5 children got 1 pen less than the others. How many pens were there in the box?

Answer 1

Answer:

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Let the no. of pens in the box be x  and the no. of pens being disrtibuted be y.

18 * y = x ;

x  + 5 =  19 * y

x + 5 = 19 * y

18 * y + 5 = 19 * y

5 = 19y - 18y

y =  5

Hence, x = 18 * 5 = 90

Answer 2

The number of pens in box = 90

Given:

A box had some pens in it

When the pens were distributed equally to 18 children none of them are  remained

When the same pens were distributed equally to 19 children 5 children got 1 pen less than the others

To find:

How many pens were there in the box?

Solution:

Let x be the number of pens in box

and y be number of pens received by 18 children equally

Given the pens were distributed equally to 18 children

⇒ 18y = x -----(1)

When the same pens were distributed equally to 19 children 5 children got 1 pen less than the others

⇒ 19y = x + 5 -----(2)

Substitute (1) in (2)

⇒ 19y = 18y + 5  

⇒ y = 5

The number of pens = 18(5) = 90

Therefore, number of pens in box = 90

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