1.

18. A two digit number is obtained by multiplying thesum of the digits by 8. Also, it is obtained bymultiplying the difference of the digits by 14 andadding 2. Find the number.​

Answer»

ANSWER:

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


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