Question

18. A two digit number is obtained by multiplying the
sum of the digits by 8. Also, it is obtained by
multiplying the difference of the digits by 14 and
adding 2. Find the number.​

Answer 1

ANSWER:

• Original number = 72

GIVEN:

• A two digit number is obtained by multiplying the
• sum of the digits by 8.
• The two digit number is obtained by
• multiplying the difference of the digits by 14 and
• adding 2.

TO FIND:

• Original number.

SOLUTION:

Let the digit at tens place be 'x'.

Let the digit at once place be 'y'.

Original number = 10x+y

CASE 1

=> 10x+y = 8(x+y)

=> 10x+y = 8x+8y

=> 10x-8x +y-8y = 0

=> 2x-7y = 0.

Muntiplying both sides by 2

=> 4x-14y = 0. .....(i)

CASE 2.

=> 10x+y = 14(x-y)+2

=> 10x+y = 14x-14y+2

=> 10x-14x+y+14y = 2

=> -4x+15y = 2

=> -4x+15y = 2

=> -4x+15y = 2 ....(ii)

Adding eq (i) and (ii)

=> 4x-14y-4x+15y = 2

=> y = 2

putting y = 2 in eq(i)

=> 4x-28 = 0

=> 4x = 28

=> x = 7

Original number = 10(7)+2

= 72