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# A positive number is 5 times another number. If 21 is added to both the numbers, 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 do:

We have to find the numbers.

Solution:

Let the smaller number be $a$

This implies,

The other number $= 5a$

Adding $21$ to both numbers, we get,

Smaller number $= a + 21$

Other number $= 5a + 21$

According to the question,

Bigger number $= 2 \times$ Smaller number

$5a + 21 = 2 \times (a + 21)$

$5a + 21 = 2a + 42$

$5a - 2a = 42 - 21$

$3a = 21$

$a = \frac{21}{3}$

$a = 7$

Therefore,

The smaller number $a=7$

The other(bigger) number $= 5a$

$= 5 \times 7$

$=35$

**The required numbers are $7$ and $35$.**

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