Answer-A two-digit number has a sum of its digits equal to 11. Additionally, if 54 is subtracted from this...

Q: Answer-A two-digit number has a sum of its digits equal to 11. Additionally, if 54 is subtracted from this...

ATQ, Let ones and tens digit of the number be a and b respectively. So, original number 10b a Reverse number 10a bSo, a b 11 --------- I And, 10b a - 54 10a b Or, 9b - 9a 54 Or, b - a 6 ---------- IIOn adding equation I and II, We get, a b b - a 11 6 Or, 2b 17 Or, b 8On putting value of b in equation I, We get, 8 a 11 Or, a 3Required number 10 8 3 83

Question

Accepted Answer

ATQ,

Let ones and tens digit of the number be 'a' and 'b' respectively.

So, original number = 10b + a

Reverse number = 10a + b

So,

a + b = 11 --------- (I)

And, 10b + a - 54 = 10a + b

Or, 9b - 9a = 54

Or, b - a = 6 ---------- (II)

On adding equation I and II,

We get, a + b + b - a = 11 + 6

Or, 2b = 17

Or, 'b' = 8

On putting value of 'b' in equation I,

We get, 8 + a = 11

Or, 'a' = 3

Required number = 10 × 8 + 3 = 83

A two-digit number has a sum of its digits equal to 11.

Solution