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GMAT Club World Cup 2026 (Day 4): A textile workshop must produce

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Saurav1408

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10 Jul 2026, 03:00

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For my convenience I am supposing that the efficiency of Standard looms be 's' and Industrial looms be 'i'

given, (7s+5i) * 14 = 1 (suppose that the total work done is equal to 1 meter of fabric prepared)

1/21s - 1/6i = 14 (as the time difference is 14 hours and each of these looms are doing the same total work - supposed as 1 meter of fabric prepared)

now if we see closely we would substitute value of 14 too
1/21s - 1/6i = 1/(7s+5i)

The equation on solving would lead to = 10i^2 - 63si - 49s^2 = 0
solving this quadratic equation we would get 490 when 70 and 7 are multiplied it would also given 63.

10i^2 - 70si + 7si - 49s^2 = 0
on rearranging we get two brackets: (i-7s) and (10i + 7s) = 0

the red highlighted would not be eligible because efficiency cannot be in negative ratio

So the correct one is green bracket; comes out to be i = 7s
i/s = 7/1

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Let standard, industrial loom rate be S and l

Combined work, w = 14(7S +5I)
Let 21 standard looms take t hours
Then 6 industrial looms take t-14 hrs

21st = 6I(t-14)
Substituting w into the above eqn
Let I/S = k

10k^2 - 63k - 49=0
(10k+7)(k-7)=0;
positive solution k=7

I/S = 7

Bunuel

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

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Let standard rate be s & industrial rate be i
Total work w = 14 (7s+5i) units

w/21s - w/6i =14
14(7s+5i) (1/21s - 1/6i) = 14
simplifying gives:
10 i^2 - 63 is - 49 s^2 =0
10i(i-7s)+7s(i-7s) =0
(i-7s)(10i+7s)=0
i=7s as i/s cannot be negative
i/s = 7

Ans D

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I'm not sure unable to solve it in my traditional way at last I just went with answer choice option and apply y(Industrial)/x (standard) = 3,5,6,7,9 and In option D I get some number that fits the equation so I went with this option choice but I loved this question this question have 2 things involved number of hours they worked and then in a hour how many rolls they will make I made my attempt it took me more than 5 mins so I feel some conceptual issue in my understanding. Good Questions to break my ego. Thanks!

Bunuel

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10 Jul 2026, 03:33

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The answer is D. 7

let s- production rate of 1 standard loom
i- production rate of 1 industrial loom
J- total work to complete the job.

1st equation from the question.
(7s+5i)14= J

2nd equation
time taken for 6 industrial loom- J/6i
and 21 standard loom J/ 21s
So, J/6i- J/21s -14

Putting 1st equation in 2nd, we get
14 (7s +5i)/6i = 14 (7s +5i)/ 21s - 14

(7s +5i)/6i = (7s +5i)/21s -1----(3)

Lets assume r= i/s

deviding the 3rd equation by s, we get

(7+5r)/6r=(7+5r)/21 -1
7(7+5r)=2r(7+5r)- 42r
49+35r=14r+10r^2 - 42r
10r^2- 63r-49=0

Factorising the equation, we get
10r^2-70r+7r-49=0
10r(r-7)+7(r-7)=0
(10r+7)(r-7)= 0
r=-7/10 or 7
hence r=7.

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10 Jul 2026, 04:35

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Let

Standard loom rate = a
Industrial loom rate = b

To find = b/a

Total work = (7a + 5b)14

Setting up equation,

$\frac{14(7a +5b)}{ 21a } - \frac{14(7a +5b)}{6b} = 14$

solving we get,

$\frac{10b}{a} - \frac{49a}{b} = 63$

try testing values,
since the RHS is multiple of 7 and one term on LHS is multiple of 7,

put b/a = 7.

equation works.

D

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10 Jul 2026, 04:44

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14*(7*standard + 5*industrial) = job

job/(21*standard) = job/(6*industrial) + 14

Subtituting job:
14*(7*standard + 5*industrial)/(21*standard) = 14*(7*standard + 5*industrial)/(6*industrial) + 14

Dividing by 14:
(7*standard + 5*industrial)/(21*standard) = (7*standard + 5*industrial)/(6*industrial) + 1
(7*standard + 5*industrial)/(21*standard) = (7*standard + 11*industrial)/(6*industrial)
(7*standard + 5*industrial)/(7*standard) = (7*standard + 11*industrial)/(2*industrial)
2*industrial*(7*standard + 5*industrial) = 7*standard*(7*standard + 11*industrial)

ratio = industrial/standard

Dividing all by standard twice:
2*ratio*(7 + 5*ratio) = 7*(7 + 11*ratio)

Checking the options 7 fits:
14*(7+35)=7*(7+77)
14*42=7*84
588=588

Answer D

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10 Jul 2026, 05:16

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Here I option D as an answer !!
- Let S = Rate of one standard room and I = Rate of one industrial room ,, WE WANT I / S which is R

---- So here are the equations 7S + 5 I = 1 / 14----- (1) and another equation is 1 / 21S - 1/6I = 14............ (2)
------- By subtracting one equation from another 1 - 2 we get 42si 10 i^2 - 63 si - 49 s^2 = 0 ,, 10 r^2 - 63 r - 49 This is dividing the entire equation by s square
( r = i /s and r^2 = (i /s)^2 )
----- now ,, from that we get (10r + 7 ) * (r - 7 ) = 0 now r = 7 means I / S = 7
---- That's how I get my answer if anybody has any better explanation feel free to tag : )

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10 Jul 2026, 05:38

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Let the rate of Standard loom be s and industrial be i. Let total work be W

In the combined case, W = R x T, Combined R = 7s+5i
W = 14(7s+5i)

Induvidually, Time for Only industrial = W/6i, for Standard = W/21s

From the question W/6i + 14 = W / 21s

Substituting W = 14(7s+5i)

14(7s + 5i)/6i + 14 = (14(7s+5i))/21

Solving for i/s we get 5.

Answer B

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10 Jul 2026, 05:46

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rate of 7 standard looms: 7st
rate of 5 industrial looms: 5in
combined: 7st + 5in

work = 14*(7st + 5in)

work/6in = work/21st - 14

14*(7st + 5in)/6in = 14*(7st + 5in)/21st - 14
(7st + 5in)/6in = (7st + 5in)/21st - 1
(7st + 5in)/6in = (-14st + 5in)/21st
21st*(7st + 5in) = 6in*(-14st + 5in)
7st*(7st + 5in) = 2in*(-14st + 5in)

ratio = in/st
in = st*ratio

7st*(7st + 5st*ratio) = 2st*ratio*(-14st + 5st*ratio)
7(7 + 5*ratio) = 2*ratio*(5*ratio - 14)
10*ratio^2 - 63*ratio - 49 = 0

Solving ratio=7 (must be positive)

The correct answer is D

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10 Jul 2026, 06:13

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total work = w
s = standard
i = industrial
ratio = r = i/s

(7s + 5i)*14 = w

equating times:
w/6i = w/21s - 14

(7s + 5i)*14/6i = (7s + 5i)*14/21s - 14
(7s + 5i)/6i = (7s + 5i)/21s - 1
(5i + 7s)/6i = (5i - 14s)/21s
(5r + 7)/6r = (5r - 14)/21
21*(5r + 7) = 6r*(5r - 14)
7*(5r + 7) = 2r*(5r - 14)
35r + 49 = 10r^2 - 28r
10r^2 - 63r - 49 = 0

The positive solution is r=7

IMO D

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10 Jul 2026, 06:36

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Here is the cleanest way to solve this question

Let the ratio of production rate of industrial loom and standard loom be k:1, and let W be the total job required

According to the question statement 1: 14(7 + 5k) = W -> Eq 1
According to the question statement 2: W/6k = W/21 - 14 => W(1/21 - 1/6k) = 14 -> Eq 2

Now, substitute the value of W from equation 1 to equation 2. Doing this will give us :-
14(7 + 5k) (1/21 - 1/6k) = 14

Cancel the 14 out from both sides and substitute the value of k from the options

Notice, initially we assumed a ratio of rates of industrial loom and standard loom, so that we can easily substitute the options and get the answer. Instead we would have to solve a huge quadratic equation

By substituting all the options, we will see that 7 satisfies the equation. Hence option D

Bunuel

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10 Jul 2026, 06:42

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Let the rate for standard looms be s and that of industrial looms be i and work be W
Combined rate is 7s+ 5i. That translates to W=14(7s+5i)
Time taken by 21 standard looms is Ts and that of 6 industrial looms is Ti. Given Ti-Ts=14
Ts= W/21s while Ti=W/6i
W/6i=W/21s-14 (Replace W with 14(7s+5i) and divide by 14 and simplify the equation to
(7s+5i)/6i= (5i-14s)/21s
Assume r=i/s meaning i=rs and substitute and simplify this 7+5r/6r= 5r-14/21
10r^2-63r-49=0
(10r+7)(r-7)=0
r=7
Ans D

Bunuel

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10 Jul 2026, 06:59

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combined rate: 7S + 5I
time: 14

14*(7S + 5I) = W

On the other hand:
W/6I + 14 = W/21S

Using both equations:
14*(7S + 5I)/6I + 14 = 14*(7S + 5I)/21S
(7S + 5I)/6I + 1 = (7S + 5I)/21S
(7S + 11I)/6I = (7S + 5I)/21S

ratio: R = I/S -> I = RS

(7 + 11R)/6R = (7 + 5R)/21

We can solve the quadratic equation or test the options:

R = 7

The answer is D

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10 Jul 2026, 07:30

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We know that,
Workshop has standard loom and industrial loom
Let,
Production rate of 1 standard loom = x
Production rate of 1 industrial loom = y
Total work required to complete the job = W

We need to find out, y / x

7 standard looms and 5b industrial looms work to ocmplete job in 14hrs
=> Work = Rate * Time
=> W = (7x + 5y)*14 ----- 1

Now,
Time it takes for 6 industrial looms working alone = W/6y
Time it takes for 21 standard looms working alone = W/21x

We are given that,
6 industrial looms take 14hrs less than 21 standard looms
=> W/6y = W/21x - 14

Substituting equation 1 here,
14*(7x+5y)/6y = 14*(7x+5y)/21x - 14
=> (7x+5y)/6y = ((7x+5y)/21x) - 1
=>7x/6y = 5y/21x - 3/2

Let y/x be a
=> 7/6a = 5a/21 - 3/2

Simplifying this we get,

=> 10a^2 - 63a - 49 = 0
=> (10a + 7)*(a - 7) = 0

Since ratio cant be negative, a =-0.7 eliminated
=>a = 7
=>y / x = 7

D. 7

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10 Jul 2026, 08:09

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Time of 7S+5I =14
Time of 6I +14 =Time of 21S
Time of 6I + Time of (7S+5I) =Time of 21S
W/6I + W/(7S+5I) = W/21S

Solving gives
I/S = 7/1
Hence (D) is the answer

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How I attempted it using the Rate, Time, Work framework

Attachments

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Why am I not getting the answer using this approach?

7/s + 5/i = 1/14
and
6/i = 21/s - 1/14

Following the above logic, I m getting i/s = 14/11. What's wrong here?

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10 Jul 2026, 12:17

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onlyPlanA

Why am I not getting the answer using this approach?

7/s + 5/i = 1/14
and
6/i = 21/s - 1/14

Following the above logic, I m getting i/s = 14/11. What's wrong here?

“14 hours less” compares times, not rates.

Please check previous pages for more.

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Bunuel What do you think of the below approach?

Rate	Time	Work
21s	t	w
6i	t-14	w
7s+5i	14	w

Find$ i/s =?$

Solving equations might take a lot of time, let's try options approach.

Options: 3,5,6,7,9

$w= (7s+5i)*14$

Let's try options, we will start with the middle one as usual.

Option	i	s	$w=(7s+5i)*14$	time for 21s	time for 6i	Difference of time
6	6	1	$w=37*14$	$w/r = \frac{(3714)}{(211)} = 28$	$w/r = \frac{(3714)}{(66)} = 10.5$	17.5Hrs
						difference >14hrs, increase industrial loom to reduce time
7	7	1	$w=42*14$	$w/r = \frac{(4214)}{(211)}=28$	$w/r = \frac{(4214)}{(76)} = 14$	14 Hrs
						This is what we were looking for.

other way is to choose to start from choice d which is 7. The reasoning behind choosing this choice is seeing numbers like 7, 14 and 21 in the question.

Answer(D)

Bunuel

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.

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Option	i	s	\(w=(7s+5i)*14\)	time for 21s	time for 6i	Difference of time
6	6	1	\(w=37*14\)	\(w/r = \frac{(3714)}{(211)} = 28\)	\(w/r = \frac{(3714)}{(66)} = 10.5\)	17.5Hrs
						difference >14hrs, increase industrial loom to reduce time
7	7	1	\(w=42*14\)	\(w/r = \frac{(4214)}{(211)}=28\)	\(w/r = \frac{(4214)}{(76)} = 14\)	14 Hrs
						This is what we were looking for.

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