A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is
a. 25
b. 72
c. 63
d. 36

Solution:

Given, the sum of a two-digit number is 9.

When 27 is added to it, the digits of the number get reversed.

We have to find the number.

Let the digit in tens place be x and unit place be y.

Sum of the digits is x + y = 9 -------------- (1)

The two digit number is of the form 10(x) + y

When 27 is added, the number gets reversed = 10(y) + x

So, 10x + y + 27 = 10y + x

10x - x + y - 10y + 27 = 0

9x - 9y + 27 = 0

Dividing by 9,

x - y + 3 = 0

x - y = -3 ------------------- (2)

Solving linear equations (1) and (2),

2x = 6

x = 6/2

x = 3

Put x = 3 in (1)

3 + y = 9

y = 9 - 3

y = 6

Therefore, the number is 36.

✦ Try This: The sum of the digits of a two-digit number is 7. If 27 is added to it, the digits of the number get reversed. The number is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.1 Sample Problem 2

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is, a. 25, b. 72, c. 63, d. 36

Summary:

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number gets reversed. The number is 36

☛ Related Questions:

Math worksheets and
visual curriculum