A factory produces nuts and bolts. A machine in it produces only nuts ...
2000 nuts are produced in 14 minutes (10 minutes break and 500 nuts per minutes so 4 minutes to produce 2000 nuts ), for next 2000 nuts it will take 14 minutes more, and for more two thousand it will take 4 minutes more, so total time = 32 minutes
similarly, 6000 bolts are produced in 20 + 5 = 25 minutes
so minimum time required is 32 minutes
View all questions of this test
A factory produces nuts and bolts. A machine in it produces only nuts ...
To find the minimum time required to produce 6000 pairs of bolts and nuts, we need to calculate the time taken by each machine to produce the required quantity and then take the maximum of those times.
1. Calculate the time taken by the machine producing nuts:
- The machine produces 500 nuts per minute.
- After producing 2000 nuts, it needs to be cleared for 10 minutes.
- So, the time taken to produce 2000 nuts is (2000 / 500) + 10 = 14 minutes.
2. Calculate the time taken by the machine producing bolts:
- The machine produces 600 bolts per minute.
- After producing 3000 bolts, it needs to be cleared for 15 minutes.
- So, the time taken to produce 3000 bolts is (3000 / 600) + 15 = 20 minutes.
3. Since the machines are operated simultaneously, the time taken by both machines will be the same.
- Let's assume the time taken to produce 6000 pairs of bolts and nuts is 't' minutes.
4. The number of nuts produced in 't' minutes by the machine producing nuts is:
- (t / 14) * 500
5. The number of bolts produced in 't' minutes by the machine producing bolts is:
- (t / 20) * 600
6. Since we need to produce 6000 pairs of nuts and bolts:
- (t / 14) * 500 = (t / 20) * 600
7. Solve the above equation to find 't':
- (t / 14) * 500 = (t / 20) * 600
- 500t = 600t / 20 * 14
- 500t = 600t / 280
- 500t * 280 = 600t
- 140000t = 600t
- 140000 = 600t - 500t
- 140000 = 100t
- t = 140000 / 100
- t = 1400
Therefore, the minimum time required to produce 6000 pairs of bolts and nuts is 1400 minutes. However, this is not one of the answer choices provided.
Let's recheck our calculations:
- (1400 / 14) * 500 = (1400 / 20) * 600
- 1000 * 500 = 70 * 600
- 500000 = 42000
It seems we made a calculation error. Let's reevaluate the problem.
The correct calculation is as follows:
6. Since we need to produce 6000 pairs of nuts and bolts:
- (t / 14) * 500 = (t / 20) * 600
7. Solve the above equation to find 't':
- 500t / 14 = 600t / 20
- 500t * 20 = 600t * 14
- 10000t = 8400t
- 8400t - 10000t = 0
- -1600t = 0
- t = 0
Therefore, the minimum time required to produce 6000 pairs of bolts and nuts is 0 minutes.
However, this does not make sense as it is not possible to produce the
A factory produces nuts and bolts. A machine in it produces only nuts ...
2000 nuts are produced in 14 minutes (10 minutes break and 500 nuts per minutes so 4 minutes to produce 2000 nuts ), for next 2000 nuts it will take 14 minutes more, and for more two thousand it will take 4 minutes more, so total time = 32 minutes
similarly, 6000 bolts are produced in 20 + 5 = 25 minutes
so minimum time required is 32 minutes