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ankushsambare
Joined: 13 Jun 2022
Last visit: 06 Sep 2026
Posts: 313
Given Kudos: 230
Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
GPA: 2.4
Products:
09 Jul 2026, 21:06
Kudos
Bookmarks
s = standard loom rate, i = industrial loom rate
w = 14(7s+5i)
w/21s - w/6i = 14
substitute w
7s+5i( 1/21s - 1/6i) = 1
let i/s = x
7+5x(1/21 - 1/6x) =1
(7+5x)(2x-7)=42x
10x^2 - 63x - 49 = 0
(10x+7)(x-7) = 0
x=7
so i/s = 7:1
Option: D
w = 14(7s+5i)
w/21s - w/6i = 14
substitute w
7s+5i( 1/21s - 1/6i) = 1
let i/s = x
7+5x(1/21 - 1/6x) =1
(7+5x)(2x-7)=42x
10x^2 - 63x - 49 = 0
(10x+7)(x-7) = 0
x=7
so i/s = 7:1
Option: D
09 Jul 2026, 21:12
Kudos
Bookmarks
D - 7
Normalize a standard loom to rate 1 and let r be the industrial rate, solving for r.
The mixed crew: W = 14(7 + 5r) = 98 + 70r
the timing gap - six industrial looms need W/(6r) hours, twenty one standard looms need W/21 and the industrial crew finishes 14 hours sooner.
W/(6r) = W/21 - 14
Denominators multiply by 42r.
7W = 2rW - 588r, so W(2r - 7) = 588r. Substitute W = 98 + 70r
(98 + 70r)(2r - 7) = 588r -> 10r^2 - 63r - 49 = 0
discriminant 3969 + 1960 - 5929 = 77^2, therefore r = (63 + 77)/20 = 7
Normalize a standard loom to rate 1 and let r be the industrial rate, solving for r.
The mixed crew: W = 14(7 + 5r) = 98 + 70r
the timing gap - six industrial looms need W/(6r) hours, twenty one standard looms need W/21 and the industrial crew finishes 14 hours sooner.
W/(6r) = W/21 - 14
Denominators multiply by 42r.
7W = 2rW - 588r, so W(2r - 7) = 588r. Substitute W = 98 + 70r
(98 + 70r)(2r - 7) = 588r -> 10r^2 - 63r - 49 = 0
discriminant 3969 + 1960 - 5929 = 77^2, therefore r = (63 + 77)/20 = 7
09 Jul 2026, 21:17
Kudos
Bookmarks
This is a work and rate problem
The formula which we generally use for solving the questions =>
Speed = Distance/ Time
Rate = Distance/Time or Rate = Work/Time (Remember the formula is the same as speed)
We also know that when 2 people are working together their rates can be added
Now using this knowledge,
let's assume for the question that the rate of 1 standard loom = x and the rate of 1 industrial loom = y
We are required to find their ratio - i.e. y:x (Industrial loom : Standard loom)
Given Information =>
(a) 7 standard and 5 industrial loom can complete the job in 14 hours
Rate = Work/Time
Work = Rate * Time
Work = (7x+ 5y)*14
(b) 6 Industrial loom take 14 hours less than 21 standard looms to complete the work
Time of 1y = Work/6y
Time of 1x = Work/21x
Work/6y = W/21x-14
now we take the info in part a,
((7x+5y)*14)/6y = ((7x+5y)*14)/21x -14
Since 14 is there in all the terms, I divide by 14,
7x+5y/6y = 7x+5y/21x - 1
Now, I solve the question by trial and error method, by replacing the rates as per question in the above, where I assume that x = 1, so y = ?
If I choose y = 6 Option c,
7+30/36 = 7+30/21 - 1
37/36 = 37/21 - 1
73/36 = 37/21
hence not correct,
Option d, y = 7
35+7/42 = 7+35/21 -1
42/42 = 42 -21/21
1 = 1
This is correct and hence Option D
The formula which we generally use for solving the questions =>
Speed = Distance/ Time
Rate = Distance/Time or Rate = Work/Time (Remember the formula is the same as speed)
We also know that when 2 people are working together their rates can be added
Now using this knowledge,
let's assume for the question that the rate of 1 standard loom = x and the rate of 1 industrial loom = y
We are required to find their ratio - i.e. y:x (Industrial loom : Standard loom)
Given Information =>
(a) 7 standard and 5 industrial loom can complete the job in 14 hours
Rate = Work/Time
Work = Rate * Time
Work = (7x+ 5y)*14
(b) 6 Industrial loom take 14 hours less than 21 standard looms to complete the work
Time of 1y = Work/6y
Time of 1x = Work/21x
Work/6y = W/21x-14
now we take the info in part a,
((7x+5y)*14)/6y = ((7x+5y)*14)/21x -14
Since 14 is there in all the terms, I divide by 14,
7x+5y/6y = 7x+5y/21x - 1
Now, I solve the question by trial and error method, by replacing the rates as per question in the above, where I assume that x = 1, so y = ?
If I choose y = 6 Option c,
7+30/36 = 7+30/21 - 1
37/36 = 37/21 - 1
73/36 = 37/21
hence not correct,
Option d, y = 7
35+7/42 = 7+35/21 -1
42/42 = 42 -21/21
1 = 1
This is correct and hence Option D
09 Jul 2026, 21:17
Kudos
Bookmarks
I set s to be the rate of a standard loom and m to be the rate of an industrial loom
(7s + 5m) = 1/14 because the can complete the job in 14 hours.
to compare individual times, let T = time for the 6 industrial looms to finish the job
6mT = 1 -> T = 1/6m
Since the 21 standard looms take 14 more hours than 6 industrial looms,
21s(T+14) = 1, sub T from the earlier equation
21s (1/6m +14) = 1 -> 21s/6m + 294s = 1 -> 7s/2m +294s =1
We can refer back to our first equation 7s + 5m = 1/14, solve for 7s and s, then sub into 7s/2m +294s =1. So
(1/14-5m)/2m +294(((1/14)-5m)/7) = 1
Simplify
1/28m - 210m = .5 multiply both sides by 28m to get rid of the fraction
1 - 5880m^2 =14m - > 5880m^2 +14m -1 =0.
Use the quadratic equation and get 1/84 as the only positive rate ( the other root -1/70 makes no sense because we are producing not taking away). so m = 1/84.
Plug into original equation to get s
7s + 5(1/84) = 1/14, s = 1/588.
The ratio of m/s = (1/84)/(1/588) which equals 7
(7s + 5m) = 1/14 because the can complete the job in 14 hours.
to compare individual times, let T = time for the 6 industrial looms to finish the job
6mT = 1 -> T = 1/6m
Since the 21 standard looms take 14 more hours than 6 industrial looms,
21s(T+14) = 1, sub T from the earlier equation
21s (1/6m +14) = 1 -> 21s/6m + 294s = 1 -> 7s/2m +294s =1
We can refer back to our first equation 7s + 5m = 1/14, solve for 7s and s, then sub into 7s/2m +294s =1. So
(1/14-5m)/2m +294(((1/14)-5m)/7) = 1
Simplify
1/28m - 210m = .5 multiply both sides by 28m to get rid of the fraction
1 - 5880m^2 =14m - > 5880m^2 +14m -1 =0.
Use the quadratic equation and get 1/84 as the only positive rate ( the other root -1/70 makes no sense because we are producing not taking away). so m = 1/84.
Plug into original equation to get s
7s + 5(1/84) = 1/14, s = 1/588.
The ratio of m/s = (1/84)/(1/588) which equals 7
