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A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number

Solution:

Considering the two-digit number as 10x + y.

Case 1:

By multiplying the sum of the digits by 8 and by subtracting 5,

8 x (x + y) - 5 = 10x + y

Using the distributive property

8x + 8y - 5 = 10x + y

2x-7y = -5--------------------(1)

Case 2:

By multiplying the difference of the digits by 16 and by adding 3,

16 x (x - y) + 3 = 10x+ y

Using the distributive property

16x - 16y + 3 = 10x + y

6x - 17y = -3-----------------(2)

Solve the linear equations (1) and (2).

Multiplying (1) by 3 and subtracting from (2),

(6x - 17y) - (6x - 21y) = - 3 - (- 15)

4y=12

y = 3.

Substituting the value of y in (1),

2x - 7 x 3 = -5

2x = 21 - 5 = 16

x = 8.

Two-digit number = 10x + y

= 10 x 8 + 3

= 80 + 3

= 83.

Therefore, the required number is 83

✦ Try This: A two-digit number is obtained by either multiplying the sum of the digits by 6 and then subtracting 3or by multiplying the difference of the digits by 12 and then adding 2. Find the number

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

NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 9

A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number

Summary:

A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. The required number is 83.

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