If 5 engines consume 6 metric tonnes of coal when each is running for

Hi Payal,

Could you elaborate how you got the consumption rate?

Thanks,

Hi Bunuel,

Are these types of questions asked in actual GMAT ? If yes, I request you to please provide an easier approach solution.

Thanks,
Ankit Singh

This is a real time GMAT question of Work-Rate problem of "Joint Variation". I need to mention that I usually proceed this type of question with a very easy approach:- ( FOLLOW THE ATTACHED DIAGRAM)
Thus,

OLD Engine ( 5) --> hrs (9) ----> MT (6)
NEW Engine (8) ---> hrs (10) ---> MT (?) , let x MT

Now 3 old engines \(\equiv\ \) 4 new engines
Hence, 8 New engine \(\equiv\ \) 6 old engines
So, the format will be:
OLD Engine ( 5) --> hrs (9) ----> MT (6)
OLD Engine (6) ---> hrs (10) ---> MT (?) , let x MT
( No. of Engine inversely proportional to hrs while MT is constant and hrs is directly proportional to MT while No. of engines are constant)
So the equation will be ( see attached image)
the equation will be 5*9*x = 6*10*6 ( x= MT of coal that we need to find out as answer)
x = 8 MT
Ans A

3 former engines are equivalent to 4 new engines. So 8 new engines are equivalent to 6 former engines.

5 engines ... 9 hours .... 6 metric tonnes
6 engines .... 10 hrs..... ??

No of metric tonnes used = 6 * (10/9) * (6/5) = 8

Answer (A)

To understand the mechanics of this method, check:
https://anaprep.com/arithmetic-work-rat ... variation/


ASR2021

If 5 engines consume 6 metric tonnes of coal when each is running for 9 hours a day, how many metric tonnes of coal will be needed for 8 engines, each running 10 hours a day, given that 3 engines of the former type consume as much as 4 engines of the latter type.

Assuming the rate of coal consumption of former engine kind per hour = X.
Assuming the rate of coal consumption of the latter engine kind per hour = Y.

Given \(3X\ =\ 4Y,\ X\ =\ \frac{4Y}{3}\) .
The total working hours for the former engine = 9*5 = 45 hours 45X = 6 metric tonnes.
For the latter engines the number of working hours = 80Y = 60X.

Since 45X requires 6 metric tonnes, 60X would require 8 metric tonnes.