Correct Answer - Option 4 : 8
Given:
The smallest 5 digit number divided by 15, 18, 24 and 14 leaves remainders respectively 5, 8, 14 and 4
Concept:
The least number which when divided by a, b and c leaves the remainder p, q and r respectively, is given by = LCM of (a, b, c) – N
Where, N = (a – p) = (b – q) = (c – r)
Calculation:
According to the question
15 - 5 = 10
18 - 8 = 10
24 = 14 = 10
14 - 4 = 10
LCM of 15, 18, 24 and 14
15 = 3 × 5
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
14 = 2 × 7
LCM = 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520
Smallest 5 digit number = 10000
Smalest 5 digit number divisible by 2520 = 10080
The number is 10080 - 10 = 1070
Sum of the digit = 1 + 0 + 0 + 7 + 0 = 8
∴ Sum of the digit is 8.
