Hi, Can anyone explain how to do these two questions?

I am not able to figure out the equation for them.

In the first question, Do we need to assume the number of new trains to be a variable? If yes, how should we proceed after that?

For the second question, I am not able to come up with a helpful equation.

Thanks!

In first question its **clearly mentioned** that 500 trains

10% already broken= 450 trains working now

How many trains working when 8% are broken= 0.92*500= 460

Trains to be added to get 460-450= 10 trains should be added

Hi Aditya, Thanks for your reply. However, the answer is 125 for the first question.

I figured it out, so 10 percent of the trains are broken, meaning 450 are working. To make the number of broken trains down to 8 percent (which means 92 percent are working) we need to add new trains. (Adding new trains means we need to add new trains to working as well as the total.)

So we setup a equation like this, 450+x/500+x = 92/100. When the solving this, we get 125 which is the correct answer.

For the second question, assuming the total distance to be 100, we can setup a equation like this, 100/ 80/85.3 + 20/57.3. Solving this we will get 77.71.

I dont think so adding 77 trains to 450 will be end up having more than 500 trains. I think trains to be added will be less than 50 in any circumstances. And you aproach seems too much convoluted

@user4209’s approach for Q1 is correct. If you add 10 trains, the percentage of broken trains is 50/510, which is not 8%.

Also your second answer is wrong. The equation you are looking for is 0.8 \times 85.3 + 0.2 \times 57.3 . That’s 79.7 km/h.

I’m still not convinced

First 10% trains were broken so it was 50 trains broken out of 500 i.e 450 trains working

To make number of broken trains to 8% 40 trains would be broken that is 50-40= 10

And to be precise why you calculating 50/460 ??

Where you should be doing (40/500)*100 ?

(40/500)*100 = 8

No. The question says that new trains are brought to reduce the *percentage* of broken trains. The number of broken trains remains the same; you are adding new trains instead.

If you add 10 trains to 450 working then it would be 92% working trains that boils down to 8% broken

Suppose you add 10 trains. We have 510 trains in total, out of which 50 are broken. 50/510 isn’t 8%.