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Q.

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?

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a

7 and 35

b

12 and 28

c

8 and 36

d

5 and 25

answer is A.

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Detailed Solution

It is given, a positive number is 5 times another number.
Let the positive number be x and the other number is 5x.
Linear equation will be x+21 and 5x+21.
If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number.
Now linear equation will be,
5x+21=2(x+21)
Solving the above equation,
5x+21=2x+42
Transposing 2x to the left hand side and 21 to the right hand side.
5x-2x=42-21
3x=21
Dividing both sides by 3.

⇒ x = 213 ⇒ x = 7

The positive number is 7 and the other number is,

5 × 7 = 35

.
Hence, the positive numbers are 7 and 35 respectively.
Correct option is 1.

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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?