Question

I. Sum of the digits is 7. Ii. Difference between the number and the number obtained by interchanging the digits is 9. Iii. Digit in the ten's place is bigger than the digit in the unit's place by 1.

Answer 1

Answer:

1. let the digit be x and y, respectively

Step-by-step explanation:

x +y = 7

Answer 2

The number according to the given conditions is 43.

• Let the digit in the units' place be x.

Let the digit in the tens' place be y.

• Sum of the digits = x + y

According to condition (i),

x + y = 7  -(i)

• The number = 10y + x

On interchanging the digits, y comes in the units' place and x comes in the tens'place.

∴  The number obtained on interchanging the digits = 10x + y

• According to condition (ii),

(10y + x) - (10x + y) = 9

Or, 10y + x - 10x - y = 9

Or, 9y - 9x = 9

Or, 9 ( y - x ) = 9

Or, y - x = 9 / 9

Or, y - x = 1  -(ii)

• According to condition (iii),

y - x = 1  -(iii)

• Adding equation -(i) and (ii), we get,

y + x = 7

y - x = 1

=> y + y + x - x = 7 + 1

Or, 2y = 8

Or, y = 8 / 2

Or, y = 4

• Putting y = 4 in equation (i), we get,

x + 4 = 7

Or, x = 7 - 4

Or, x = 3

• Therefore, the number 10y + x = (10 × 4) + 3

Or, 40 +3 = 43