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

Question

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.

A. 8
B. 9
C. 12
D. 12.5
E. 14.2

A. 8 
B. 9 
C. 12 
D. 12.5 
E. 14.2

Archit3110 · Answer

use
m1*t1/w1 = m2*t2/w2
solve w2 = 8*3/4
and given then given that 3 engines of the former type consume as much as 4 engines of the latter type.
so answer IMO A ; 8

EgmatQuantExpert · Answer

Solution

Given  
 • 5 engines consume 6 metric tonnes of coal when each is running for 9 hours a day
• 3 engines of the former type consume as much as 4 engines of the latter type

To find  
 • How many metric tonnes of coal will be needed for 8 engines, each running 10 hours a day?

Approach and Working out  
We have:
 • Direct relation between engine and coal: more engine – more coal
• Direct relation between hours and coal: more hours per day – more coal
• Direct relation between rate of consumption and coal: more consumption – more coal

Ratio of engines = 5: 8
Ratio of hours per day = 9: 10
Ratio of consumption rate = (1/3): (1/4)
These ratios are equal to 6: n

Therefore,
 • n = 8 x 10 x ¼ x 6 x 1/5 x 1/9 x 3
Or, n = 8

Thus, option A is the correct answer.

Correct Answer: Option A

mjsoriano · Answer

Hi Payal,

Could you elaborate how you got the consumption rate?

Thanks,

ASR2021 · Answer

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

bobnil · Answer

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

KarishmaB · Answer

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

GmatPoint · Answer

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.

A. 8
B. 9
C. 12
D. 12.5
E. 14.2

﻿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.

Apoorva0406 · Answer

consider, the formula (m1*t1)/w1 = (m2*t2)/w2
also, 3 old machines = 4 new machines.
 6 old machines = 8 new machines.
m1= old machines, t1= time run, w1 = work or coal consumed.
therefore, (5*9)/8 = (6*10)/w2; 
 w2 = 8.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards