Over here I did cross multiplication

24 Problems β 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

Over here I did cross multiplication

24 Problems β 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

Letβs 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.

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**

1 Like

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!

1 Like

Thank you very much.

1 Like