Can you explain this? Can’t seem to crack it
Andrew can finish making a pizza in ‘x’ hours working at a constant rate. Barry can finish a pizza in ‘y’ hours working at a constant rate. If Andrew works for ‘z’ hours and is then joined by Barry until 50 pizzas are finished, for how long will Barry and Andrew operate simultaneously?
- (50xy-z)/(x+y)
- y(50x-z)/(x+y)
- 50y(x-z)/(x+y)
- (x+y)/(50xy-z)
- (x+y-z)/(50xy)
Hi Chaitanya,
This question you can solve using, Plugging In or Normal approach,
It’s very important for these types of questions to follow a step by step approach.
Let’s draw the rate chart here,
| Work = Rate * Time | |||
| Person | Work | time | Rate |
| Andrew | 1 | x | 1/x |
| Barry | 1 | y | 1/y |
If Andrew for “z” hours then he would complete (z/x) no. of pizzas.
Total work is to complete 50 pizzas,
Since Andrew would have completed (z/x) number of pizzas,
Then the remaining pizzas would 50-(z/x) = (50x-z)/x
No Barry also working along with Andrew to complete the remaining pizza,
We should find the time taken for them to complete this,
Time taken = Work/rate
= ((50x-z)/x)/ (1/x+1/y)
= ((50x-z)/x)/(x+y/xy)
= ((50x-z)y)/(x+y)
So the answer is B.
We can also do plugging-in
Let us say x = 10, y = 50
Given, Andrew can make 1/10 pizza every hour
Barry can make 1/50 pizza every hour
Let us say z = 100.
Now Andrew has already made 10 pizzas and 40 pizzas are left which are to be made by both Andrew and Barry. They together will operate for 40/(1/10 + 1/50) hours, which is equal to 1000/3. The values match with our answer option:
y (50x – z)/(x+y) = 50(500 – 100)/(60) = 50(400)/(60) = 1000/3.
So the answer is B.
Hope it is clear.
