A certain sum of money is suffecient to pay either Austin's wage for 12 days…
2024
A certain sum of money is suffecient to pay either Austin's wage for 12 days or Daniel's wage for 18 days . For how long will it suffice if both Austin and daniel work together ?
- A.
5(1/2)
- B.
8(2/3)
- C.
7(1/5)
- D.
6(1/4)
Attempted by 754 students.
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Correct answer: C
Answer: 7 (1/5) days.
Method 1 (numerical example):
Take the total sum as Rs. 72 (LCM of 12 and 18) to make calculations simple.
Austin's daily wage = 72 ÷ 12 = Rs. 6.
Daniel's daily wage = 72 ÷ 18 = Rs. 4.
Together they earn 6 + 4 = Rs. 10 per day.
So the sum lasts 72 ÷ 10 = 7.2 days = 7 1/5 days.
Method 2 (algebraic):
Let the total sum be x. Austin's daily share is x/12 and Daniel's is x/18.
Combined daily share = x/12 + x/18 = (3x + 2x)/36 = 5x/36.
The number of days the sum will last = x ÷ (5x/36) = 36/5 = 7.2 = 7 1/5.