If the difference between- a two digit number AB and the number obtained by reversing its digits ie, BA = CD, then
C + D =
If the difference between- a two digit number AB and the number obtained by reversing its digits ie, BA = CD, then
C + D =
The correct option is C 9
In a 2 digit number, the difference between the original number and the number formed after reversing the digits will always have two digits which will be less than 99.
In the given question:
CD = (10A + B) - (10B + A)
= 10A + B -10B - A = 9A - 9B
Hence CD = 9(A - B)
i.e. their difference is always divisible by 9.
There is an interesting pattern for multiples of 9.
9 × 1 = 9 = 10 × 0 + 1 × 9 → 0 + 9 = 9
9 × 2 = 18 = 10 × 1 + 1 × 8 → 8 + 1 = 9
9 × 3 = 27 = 10 × 2 + 1 × 7 → 2 + 7 = 9
.
.
.
.9 × 10 = 90 = 10 × 9 + 1 × 0 → 9 + 0 = 9
Since CD is a multiple of 9, C + D = 9 as observed from the above pattern.
In a 2 digit number, the difference between the original number and the number formed after reversing the digits will always have two digits which will be less than 99.
In the given question:
CD = (10A + B) - (10B + A)
= 10A + B -10B - A = 9A - 9B
Hence CD = 9(A - B)
i.e. their difference is always divisible by 9.
There is an interesting pattern for multiples of 9.
9 × 1 = 9 = 10 × 0 + 1 × 9 → 0 + 9 = 9
9 × 2 = 18 = 10 × 1 + 1 × 8 → 8 + 1 = 9
9 × 3 = 27 = 10 × 2 + 1 × 7 → 2 + 7 = 9
.
.
.
.9 × 10 = 90 = 10 × 9 + 1 × 0 → 9 + 0 = 9
Since CD is a multiple of 9, C + D = 9 as observed from the above pattern.
