The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number Class 9

The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number Class 9

Question 1.

The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. Find both the numbers. Class 9

Solution:

Let the digit is tens place be a and the digit in units place be b.

∴ The two digit number is 10a + b.

According to the given condition,

a - b = 3

∴ a = 3 + b ... (i)

If the digits are interchanged, the new number is, 10b + a.

According to the second condition,

10a + b + 10b + a = 143

∴ 11a + 10b = 143

∴ 11 (a + b) = 143

∴ a + b = $\frac{143}{11}$

∴ a + b = 13 ... (ii)

Substituting a = b + 3 in (ii), we get

(b + 3) + b = 13

∴ 2b + 3 = 13

∴ 2b = 13 - 3

∴ 2b = 10

∴ b = $\frac{10}{2}$ = 5

Now, substituting b = 5 in (i), we get

a = 5 + 3 = 8

Original number = 10a + b = 10(8) + 5

= 80 + 5 = 85

∴ The two numbers are 85 and 58.