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?

Solution:

Let the digits at tens place and ones place be x and 9 - x

Therefore, original number = 10x + (9 - x) = 9x + 9

On interchanging the digits, the digits at ones place and tens place will be x and 9 - x respectively.

Therefore, the new number after interchanging the digits = 10(9 - x) + x = 90 - 9x

New number = Original number + 27

90 - 9x = 9x + 9 + 27

90 - 9x = 9x + 36

Transposing 9x to RHS and 36 to LHS, we obtain

90 - 36 = 18x

54 = 18x

Dividing both sides by 18, we obtain

x = 3

Hence, 9 - x = 6

Hence, the digits at tens place and one's place of the number are 3 and 6 respectively. The number is 36.

Video Solution:

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?

NCERT Solutions Class 8 Maths Chapter 2 Exercise 2.4 Question 3

Summary:

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. The two-digit number is 36.

☛ Related Questions:

• 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?
• Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ₹50 per metre and trouser material that costs him ₹90 per metre. For every 3 meters of the shirt material he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹36,600. How much trouser material did he buy?