for earl
JA two digit no is obtained by either multiplying
the sum of the digits by 8 and then substracting
by 5.7or [by multiplying the diffrence of digits
bu 16 and adding 3] for ea cid
solving part
Answers
Answer:-
Let the number be (10x + y).
Given:
Case - 1:
The number is obtained by multiplying the sum of the digits by 8 and subtracting 5.
→ (sum of the digits) * 8 - 5 = number
→ 8(x + y) - 5 = 10x + y
→ 8x + 8y - 5 = 10x + y
→ 8y - 5 - y = 10x - 8x
→ 2x = 7y - 5
→ x = (7y - 5) / 2 -- equation (1)
Case - 2:
It is formed by multiplying the difference of the digits by 16 and adding 3.
→ 16 ( Difference of the digits) + 3 = number
→ 16(x - y) + 3 = 10x + y
→ 16x - 16y + 3 = 10x + y
→ 16x - 10x + 3 = y + 16y
→ 6x + 3 = 17y
Substitute the value of x from equation (1).
→ 6[ (7y - 5) / 2 ] + 3 = 17y
→ 3(7y - 5) + 3 = 17y
→ 21y - 15 + 3 = 17y
→ 21y - 12 = 17y
→ 21y - 17y = 12
→ 4y = 12
→ y = 12/4
→ y = 3
Putting the value of y in equation (1) we get,
→ x = (7y - 5)/2
→ x = [ 7(3) - 5 ] / 2
→ x = (21 - 5)/2
→ x = 16/2
→ x = 8
The number = 10(8) + 3 = 80 + 3 = 83.
Hence, the required number is 83.