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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
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
10 Jul 2026, 03:06
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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
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
10 Jul 2026, 03:24
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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
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
10 Jul 2026, 03:27
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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
