Over here I did cross multiplication
24 Problems → 15 mins
x problems ----> 40 mins
24 x 40 = 15x
Why is the ans incorrect when the same method is applied in the two sums below
What is wrong in my logic
Let’s consider this problem:
If we apply the cross multiplication method, we get
24 days - 15 workers
x days - 40 workers
x = \frac{24\times40}{15}
This results in 64, implying that 40 workers take 64 days. This is logically not right, since 40 workers are taking more days than 15 workers.
I would recommend solving the problem using the work formula i.e work = rate \times time. This would give the right solution for all 3 types of problems.
Solutions:
rate = 15 workers
time = 24 days
work = 15 x 24
New rate = 40 workers
time = work/rate = (15 x 24)/40 = 9 days
Ans: B
Problem 2:
Here, we could use cross multiplication for finding the rate since they have given the rate for 18 driveways instead of 1
For 18 driveways - 15 workers
1 driveway = 15/18
Rate = 15/18
Work = 15/18 x 24 = 20 days
Now,
For 40 driveways - 22 workers assigned
1 driveway - 40/22 workers
The new rate is 40/22
20 = 40/22 x time
time = (20x22)/40 = 11 days
Ans: C
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Thank you so much for this solution. I am very grateful to you 
When we say rate, we speak abt workers as an entity right
what other entities could be considered as rate
Yes, you are right
Some similar entities which I can think of off the top of my head would be -
- taps - where they say a tap takes x hours to fill a tank or drain a tank.
- The work formula could also be used for speed problems, as distance = speed x time - here the speed is the rate and distance is the work.
I will add more if I remember them!
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Thank you very much.
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