A earns 25% more than B. C earns 25% more than A. A earns 20% more than D. E…
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A earns 25% more than B. C earns 25% more than A. A earns 20% more than D. E earns 20% more than A. A, B, C, D, and E earn integer amounts less than Rs. 100. What is the total amount earned by all five of them put together?
Answer: C. Rs. 305 — Plan: Express every income in terms of A and use the integer and less-than-100 constraints to determine A. B = (4/5)A, so A must be a multiple of 5 for B to…
- A.
Rs. 300
- B.
Rs. 245
- C.
Rs. 305
- D.
Rs. 480
Attempted by 78 students.
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Correct answer: C
Plan: Express every income in terms of A and use the integer and less-than-100 constraints to determine A.
B = (4/5)A, so A must be a multiple of 5 for B to be an integer.
C = (5/4)A, so A must be a multiple of 4 for C to be an integer.
D = (5/6)A, so A must be a multiple of 6 for D to be an integer.
E = (6/5)A, so A must be a multiple of 5 for E to be an integer.
Therefore A must be a multiple of lcm(4,5,6) = 60. The only multiple of 60 less than 100 is 60, so A = 60.
Compute the others:
A = 60
B = (4/5) × 60 = 48
C = (5/4) × 60 = 75
D = (5/6) × 60 = 50
E = (6/5) × 60 = 72
Total = 60 + 48 + 75 + 50 + 72 = 305
Answer: Rs. 305