UPSC CAPF Assistant Commandant Model Paper 3

GIVEN:
A 3-digit number 7P7 is added to 94Q to get a 4 digit number 1Q83.
1Q83 is divisible by 9.
CONCEPT:
Divisibility by 9:
If the sum of digits is divisible by 9, the number will be divisible by 9 too.
CALCULATION:
Applying the divisibility by 9:
(1 + Q + 8 + 3) is divisible by 9
Or
(12 + Q) is divisible by 9.
Here, only possible value of Q = 6 as (12 + 6) = 18 is divisible by 9.
Hence,
Q = 6
Now,
7P7 is added to 94Q i.e. 946 to get a 4 digit number 1Q83 i.e. 1683.
Hence,
1683 – 946 = 7P7
⇒ 737 = 7P7
So,
P = 3
∴ Q – P = 6 – 3 = 3