A takes 10 days less
together, they can finish the work in 12 days, find the time taken
17. A train covers a distance of 360 km at a uniform speed. If the speed of the train is increased
by 5 km/h, it takes 48 minutes less in the journey to cover the same distance. Find the original
speed of the train.
Answers
Correct Question:
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Given:
- A takes 10 days less than the time taken by B to finish a work.
To find:
- Time taken by B to finish the work if A and B together finish the work in 12 days.
Assumptions:
- Let B take x days to complete the piece of work.
- Hence, A take (x-10) days to finish the work.
According to the question,
➮ 1/x+1/(x-10) = 1/12
On taking LCM,
➮ (x-10)+x/x(x-10) = 1/12
➮ 2x-10/x²-10x = 1/12
On Cross multiplying the equation:
➮ x²-10x = 12(2x-10)
➮ x²-10x = 24x-120
➮ x² = 24x+10x-120
➮ x² = 34x-120
➮ x²-34x+120 = 0
On factorizing the equation,
➮ x²-30x-4x+120 = 0
➮ x(x-30)-4(x-30) = 0
➮ (x-4)(x-30) = 0
➮ x-4 = 0 or x-30 = 0
➮ x = 4 or x = 30
Let us apply the value of 4 in (x-10) [Work done by A]
➮ A = (x-10)
➮ A = (4-10)
➮ A = -6
We know that time cannot be negative. Therefore, x = 4 is rejected.
Hence, x = 30. This implies that B can work in 30 number of days.
Request:
- Sorry for not answering your second question. Kindly, ask your queries one by one. Thanks!