A Positive number is 5 times another number. if 21 is added to both the number, then one of the new numbers becomes twice the other new number. what are the numbers?

Given: A Positive number is 5 times another number and if 21 is added to both the numbers, then one of the new numbers becomes twice the other new number.

To find: We have to find the numbers.

Solution: 

Let the smaller number = a

So, the bigger number = 5a

Adding 21 to both numbers

Smaller number = a + 21

Bigger number = 5a + 21

Now, according to the problem:

Bigger number = 2 x Smaller number

5a + 21 = 2 x (a + 21)

5a + 21 = 2a + 42

5a - 2a = 42 - 21

3a = 21

a = $\frac{21}{7}$

a = 7

Therefore,

The smaller number = a = 7

The bigger number = 5a = 5 x 7 = 35

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Updated on: 10-Oct-2022

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