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