AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8 then what is A + B + C equal to ?

(UPSC CSAT – 2023)

1. 6
2. 7
3. 8
4. 9

Solution: Ans.(1)

So D & G should have the value 4 and 5 (not necessary in same order)

The value of D can not be 5, because when we multiply D & B, it can not make 8 (F), So D = 4 & G = 5.

Then B should be 2, which make D×B=8,

All the digits are distinct, therefore  A and C would have any values of  1, 3 or 9.

But as we can see that 12×34 = 408

Therefore A=1 & C=3

Hence A+B+C = 1+2+3 = 6