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The ratio of the efficiencies of P, Q and R is 2 : 3 : 5. The total wages of P, Q and R for working for 14, 24 and 20 days respectively are Rs. 6000. Find the total wages of the three, when P working for 9 days, Q for 14 days and R for 8 days.
- a)3000
- b)2860
- c)2450
- d)3240
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The ratio of the efficiencies of P, Q and R is 2 : 3 : 5. The total wa...
Ratio of the work done by P, Q and R = (2 × 14) : (3 × 24) : (5 × 20) = 7 : 18 : 25
Total wage of P = {7/50} × 6000 = 840
∴ Daily wages of P = 840/14 = 60
Similarly,
Daily wages of Q = (18/20) × (1/24) × 6000 = 90
Daily wages of R = (25/50) × (1/20) × × 6000 = 150
∴ Total wages of P, Q and R working for the given periods = (60 × 9) + (90 × 14) + (150 × 8) = 3000
Most Upvoted Answer
The ratio of the efficiencies of P, Q and R is 2 : 3 : 5. The total wa...
Given:
Efficiency ratio of P, Q and R = 2 : 3 : 5
Total wages of P, Q and R for working for 14, 24 and 20 days respectively = Rs. 6000
To find:
Total wages of P, Q and R when P works for 9 days, Q for 14 days and R for 8 days
Solution:
Let the efficiency of P be 2x, Q be 3x and R be 5x
Let the wages per day of P, Q and R be a, b and c respectively
Given,
2x * 14a + 3x * 24b + 5x * 20c = 6000
28xa + 72xb + 100xc = 6000
7xa + 18xb + 25xc = 1500 ...(1)
Now, we need to find the total wages of P, Q and R when P works for 9 days, Q for 14 days and R for 8 days.
Total wages of P, Q and R = 9a + 14b + 8c
To find the values of a, b and c, we can use the efficiency ratios.
Efficiency of P:Q:R = 2:3:5
Let us assume that P works for 1 day.
Then, Q will work for (3/2) days and R will work for (5/2) days.
Let the wages per day of P be x.
Then, wages per day of Q will be (2/3)x and wages per day of R will be (2/5)x.
Let us assume that the total wages of P, Q and R for working for 1 day each is y.
Then,
x + (2/3)x + (2/5)x = y
31x/15 = y
x = 15y/31
Therefore,
Wages per day of P = x = (15/31) * y
Wages per day of Q = (2/3)x = (10/31) * y
Wages per day of R = (2/5)x = (6/31) * y
Now, we can substitute the values of a, b and c in equation (1) to get the value of y.
7[(15/31) * y] + 18[(10/31) * y] + 25[(6/31) * y] = 1500
105y + 180y + 150y = 1500 * 31
435y = 46500
y = 100
Therefore,
Wages per day of P = (15/31) * 100 = Rs. 48.39
Wages per day of Q = (10/31) * 100 = Rs. 32.26
Wages per day of R = (6/31) * 100 = Rs. 19.35
Total wages of P, Q and R when P works for 9 days, Q for 14 days and R for 8 days
= 9 * 48.39 + 14 * 32.26 + 8 * 19.35
= Rs. 435.51 + Rs. 451.64 + Rs. 154.8
Efficiency ratio of P, Q and R = 2 : 3 : 5
Total wages of P, Q and R for working for 14, 24 and 20 days respectively = Rs. 6000
To find:
Total wages of P, Q and R when P works for 9 days, Q for 14 days and R for 8 days
Solution:
Let the efficiency of P be 2x, Q be 3x and R be 5x
Let the wages per day of P, Q and R be a, b and c respectively
Given,
2x * 14a + 3x * 24b + 5x * 20c = 6000
28xa + 72xb + 100xc = 6000
7xa + 18xb + 25xc = 1500 ...(1)
Now, we need to find the total wages of P, Q and R when P works for 9 days, Q for 14 days and R for 8 days.
Total wages of P, Q and R = 9a + 14b + 8c
To find the values of a, b and c, we can use the efficiency ratios.
Efficiency of P:Q:R = 2:3:5
Let us assume that P works for 1 day.
Then, Q will work for (3/2) days and R will work for (5/2) days.
Let the wages per day of P be x.
Then, wages per day of Q will be (2/3)x and wages per day of R will be (2/5)x.
Let us assume that the total wages of P, Q and R for working for 1 day each is y.
Then,
x + (2/3)x + (2/5)x = y
31x/15 = y
x = 15y/31
Therefore,
Wages per day of P = x = (15/31) * y
Wages per day of Q = (2/3)x = (10/31) * y
Wages per day of R = (2/5)x = (6/31) * y
Now, we can substitute the values of a, b and c in equation (1) to get the value of y.
7[(15/31) * y] + 18[(10/31) * y] + 25[(6/31) * y] = 1500
105y + 180y + 150y = 1500 * 31
435y = 46500
y = 100
Therefore,
Wages per day of P = (15/31) * 100 = Rs. 48.39
Wages per day of Q = (10/31) * 100 = Rs. 32.26
Wages per day of R = (6/31) * 100 = Rs. 19.35
Total wages of P, Q and R when P works for 9 days, Q for 14 days and R for 8 days
= 9 * 48.39 + 14 * 32.26 + 8 * 19.35
= Rs. 435.51 + Rs. 451.64 + Rs. 154.8
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The ratio of the efficiencies of P, Q and R is 2 : 3 : 5. The total wages of P, Q and R for working for 14, 24 and 20 days respectively are Rs. 6000. Find the total wages of the three, when P working for 9 days, Q for 14 days and R for 8 days.a)3000b)2860c)2450d)3240Correct answer is option 'A'. Can you explain this answer?
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