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23 Feb 2024, 02:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
72% (03:08) correct
28%
(02:59)
wrong
based on 197
sessions
History
Date
Time
Result
Not Attempted Yet
Rohit, Harsha and Sanjeev are three typists who working simultaneously can type 216 pages in four hours. In one hour Sanjeev can type as many pages more than Harsha as Harsha can type more than Rohit, During a period of five hours Sanjeev can type as many pages as Rohit can during seven hours. How many pages does each of them type per hour?
(A) 16, 18, 22
(B) 14, 17, 20
(C) 15, 17, 22
(D) 15, 18, 21
(E) None of these
(A) 16, 18, 22
(B) 14, 17, 20
(C) 15, 17, 22
(D) 15, 18, 21
(E) None of these
jack5397
Joined: 13 Sep 2020
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Location: India
Concentration: General Management, Strategy
Schools: ISB '27 IIMA '26 INSEAD '26
GMAT Focus 1: 575 Q79 V79 DI77 
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23 Feb 2024, 04:33
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IMO - D
Good question to teach us the importance of careful reading of question.
Given :
216 pages in 4 hours combined by R,H & S.
one hour S can type as many pages more than H as H can type more than R.
period of five hours S can type as many pages as R can during seven hours - This basically gives us the ratio of time taken to type same number of pages which gives the biggest hint for the rates to type to number of pages.
S*5 = R*7
S:R = 7:5
Now check the options for this ratio only option D qualifies. To make sure this is the correct option and not E. Understand the second sentence [one hour S can type as many pages more than H as H can type more than R.]
Hence option D.
Good question to teach us the importance of careful reading of question.
Given :
216 pages in 4 hours combined by R,H & S.
one hour S can type as many pages more than H as H can type more than R.
period of five hours S can type as many pages as R can during seven hours - This basically gives us the ratio of time taken to type same number of pages which gives the biggest hint for the rates to type to number of pages.
S*5 = R*7
S:R = 7:5
Now check the options for this ratio only option D qualifies. To make sure this is the correct option and not E. Understand the second sentence [one hour S can type as many pages more than H as H can type more than R.]
Hence option D.
08 Sep 2024, 18:35
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Bookmarks
Rohit, Harsha and Sanjeev are three typists who working simultaneously can type 216 pages in four hours
Let Rate of Rohit = R, Rate of Harsha = H and Rate of Sanjeev = S
When they work together their rate gets added up.
=> Combined Rate = R + H + S
Rate * Time = Work
=> (R + H + S) * 4 = 216
=> R + H + S = 216/4 = 54
In one hour Sanjeev can type as many pages more than Harsha as Harsha can type more than Rohit
Let Rate Harsha can type x more pages/hour than Rohit
=> H = R + x
=> S = H + X = R + 2x
During a period of five hours Sanjeev can type as many pages as Rohit can during seven hours.
=> Work done by Sanjeev in 5 hours = Work done by Rohit in 7 hours
=> S * 5 = R * 7
=> (R + 2x) * 5 = R * 7
=> 5R + 10x = 7R
=> 2R = 10x
=> R = 5x
R + H + S = 54
=> R + (R + x ) + (R + 2x) = 54
=> 3R + 3x = 54 = 3 * 18
=> R + x = 18
=> 5x + x = 18
=> 6x = 18
=> x = 3
=> R = 5*3 = 15
=> H = R + x = 15 + 3 = 18
=> S = R + 2x = 15 + 2*3 = 15 + 6 = 21
So, Answer will be D
Hope it helps!
Watch following video to MASTER Work Rate Problems
Let Rate of Rohit = R, Rate of Harsha = H and Rate of Sanjeev = S
When they work together their rate gets added up.
=> Combined Rate = R + H + S
Rate * Time = Work
=> (R + H + S) * 4 = 216
=> R + H + S = 216/4 = 54
In one hour Sanjeev can type as many pages more than Harsha as Harsha can type more than Rohit
Let Rate Harsha can type x more pages/hour than Rohit
=> H = R + x
=> S = H + X = R + 2x
During a period of five hours Sanjeev can type as many pages as Rohit can during seven hours.
=> Work done by Sanjeev in 5 hours = Work done by Rohit in 7 hours
=> S * 5 = R * 7
=> (R + 2x) * 5 = R * 7
=> 5R + 10x = 7R
=> 2R = 10x
=> R = 5x
R + H + S = 54
=> R + (R + x ) + (R + 2x) = 54
=> 3R + 3x = 54 = 3 * 18
=> R + x = 18
=> 5x + x = 18
=> 6x = 18
=> x = 3
=> R = 5*3 = 15
=> H = R + x = 15 + 3 = 18
=> S = R + 2x = 15 + 2*3 = 15 + 6 = 21
So, Answer will be D
Hope it helps!
Watch following video to MASTER Work Rate Problems
