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D
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A textile workshop must produce a certain number of identical fabric rolls. The workshop has standard looms and industrial looms. Each standard loom produces fabric at the same constant rate, and each industrial loom produces fabric at the same constant rate. If 7 standard looms and 5 industrial looms, working together, can complete the job in 14 hours, and 6 industrial looms working alone can complete the job in 14 hours less time than 21 standard looms working alone, what is the ratio of the production rate of one industrial loom to the production rate of one standard loom?
A. 3
B. 5
C. 6
D. 7
E. 9
A. 3
B. 5
C. 6
D. 7
E. 9
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M46-38
09 Jul 2026, 09:00
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GMAT Club Official Solution:
A textile workshop must produce a certain number of identical fabric rolls. The workshop has standard looms and industrial looms. Each standard loom produces fabric at the same constant rate, and each industrial loom produces fabric at the same constant rate. If 7 standard looms and 5 industrial looms, working together, can complete the job in 14 hours, and 6 industrial looms working alone can complete the job in 14 hours less time than 21 standard looms working alone, what is the ratio of the production rate of one industrial loom to the production rate of one standard loom?
A. 3
B. 5
C. 6
D. 7
E. 9
Let x and y be the production rates of one standard loom and one industrial loom, respectively.
We need to find y/x.
Since 7 standard looms and 5 industrial looms complete the job in 14 hours, the total work is:
work = time * combined rate = 14(7x + 5y)
So 21 standard looms working alone would take:
time = work/rate = 14(7x + 5y)/(21x) = 2(7x + 5y)/(3x) hours
And 6 industrial looms working alone would take:
time = work/rate = 14(7x + 5y)/(6y) = 7(7x + 5y)/(3y) hours
Since 6 industrial looms complete the job in 14 hours less time than 21 standard looms, we have:
2(7x + 5y)/(3x) - 7(7x + 5y)/(3y) = 14
Multiply both sides by 3xy:
2y(7x + 5y) - 7x(7x + 5y) = 42xy
14xy + 10y^2 - 49x^2 - 35xy = 42xy
10y^2 - 63xy - 49x^2 = 0
Since we need to find y/x, divide by x^2:
10(y/x)^2 - 63(y/x) - 49 = 0
At this stage, it is easier to test the answer choices for y/x than to solve the quadratic. Only answer choice D works:
10(7)^2 - 63(7) - 49 = 490 - 441 - 49 = 0
Therefore, y/x = 7, and thus the ratio of the production rate of one industrial loom to the production rate of one standard loom is 7.
Answer: D.
A textile workshop must produce a certain number of identical fabric rolls. The workshop has standard looms and industrial looms. Each standard loom produces fabric at the same constant rate, and each industrial loom produces fabric at the same constant rate. If 7 standard looms and 5 industrial looms, working together, can complete the job in 14 hours, and 6 industrial looms working alone can complete the job in 14 hours less time than 21 standard looms working alone, what is the ratio of the production rate of one industrial loom to the production rate of one standard loom?
A. 3
B. 5
C. 6
D. 7
E. 9
Let x and y be the production rates of one standard loom and one industrial loom, respectively.
We need to find y/x.
Since 7 standard looms and 5 industrial looms complete the job in 14 hours, the total work is:
work = time * combined rate = 14(7x + 5y)
So 21 standard looms working alone would take:
time = work/rate = 14(7x + 5y)/(21x) = 2(7x + 5y)/(3x) hours
And 6 industrial looms working alone would take:
time = work/rate = 14(7x + 5y)/(6y) = 7(7x + 5y)/(3y) hours
Since 6 industrial looms complete the job in 14 hours less time than 21 standard looms, we have:
2(7x + 5y)/(3x) - 7(7x + 5y)/(3y) = 14
Multiply both sides by 3xy:
2y(7x + 5y) - 7x(7x + 5y) = 42xy
14xy + 10y^2 - 49x^2 - 35xy = 42xy
10y^2 - 63xy - 49x^2 = 0
Since we need to find y/x, divide by x^2:
10(y/x)^2 - 63(y/x) - 49 = 0
At this stage, it is easier to test the answer choices for y/x than to solve the quadratic. Only answer choice D works:
10(7)^2 - 63(7) - 49 = 490 - 441 - 49 = 0
Therefore, y/x = 7, and thus the ratio of the production rate of one industrial loom to the production rate of one standard loom is 7.
Answer: D.
General Discussion
09 Jul 2026, 08:26
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Rs= rate of standard loom
Ri= rate of industrial loom
tt time for 21 s looms
7s+5i=14hrs
7s*3=21
PITA
starting with the second largest 7
1i=7s so 5i=35s
checking tt= 7s=35s=42s
if 42s=14hrs then 21s=14*2=28hrs
verify
time 6i=t21s-14hrs
time 6i=28-14=14hrs
6i=6*7=42 s
ans D 7
Ri= rate of industrial loom
tt time for 21 s looms
7s+5i=14hrs
7s*3=21
PITA
starting with the second largest 7
1i=7s so 5i=35s
checking tt= 7s=35s=42s
if 42s=14hrs then 21s=14*2=28hrs
verify
time 6i=t21s-14hrs
time 6i=28-14=14hrs
6i=6*7=42 s
ans D 7
09 Jul 2026, 08:28
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Let the production rate of standard loom and industrial loom be x & y fabric rolls / hour. Let y/x = k
The number of fabric rolls to be produced = 14(7x + 5y)
The number of hours taken by 6 industrial looms = 14(7x+5y)/6y = 7(7x+5y)/3y = 7/3 (7x/y +5) = 7(7/k + 5)/3
The number of hours taken by 21 standard looms = 14(7x+5y)/21x = 2/3 (7 + 5y/x) = 2(7+5k)/3
2(7+5k)/3 - 7(7/k + 5)/3 = 14
(14 + 10k) - (49/k + 35) = 42
10k - 49/k = 42 + 35 - 14 = 63
10k^2 - 63k - 49 = 0
k = 7 or -0.7
k = 7 since -0.7 is not feasible since production rates are +ve.
The ratio of production rate of one industrial loom to the production rate of one standard loom = 7
IMO D
The number of fabric rolls to be produced = 14(7x + 5y)
The number of hours taken by 6 industrial looms = 14(7x+5y)/6y = 7(7x+5y)/3y = 7/3 (7x/y +5) = 7(7/k + 5)/3
The number of hours taken by 21 standard looms = 14(7x+5y)/21x = 2/3 (7 + 5y/x) = 2(7+5k)/3
2(7+5k)/3 - 7(7/k + 5)/3 = 14
(14 + 10k) - (49/k + 35) = 42
10k - 49/k = 42 + 35 - 14 = 63
10k^2 - 63k - 49 = 0
k = 7 or -0.7
k = 7 since -0.7 is not feasible since production rates are +ve.
The ratio of production rate of one industrial loom to the production rate of one standard loom = 7
IMO D
