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?

Solution:

Let the numbers be x and 5x.

Since x + 21 is smaller than 5x + 21, therefore according to the question,

21 + 5x = 2(x + 21)

21 + 5x = 2x + 42

Transposing 2x to LHS and 21 to RHS, we obtain

5x - 2x = 42 - 21

3x = 21

Dividing both sides by 3, we obtain

x = 7

First number is x = 7

Second number is 5x = 5 × 7 = 35

Hence, the numbers are 7 and 35 respectively.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 2

Video Solution:

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?

NCERT Solutions Class 8 Maths Chapter 2 Exercise 2.4 Question 2

Summary:

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. The two positive numbers are 7 and 35.

☛ Related Questions:

• Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
• One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
• Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?
• There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate ₹100 per metre it will cost the village panchayat ₹ 75000 to fence the plot. What are the dimensions of the plot?