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8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work?
Most Upvoted Answer
8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 b...
Let the time taken by girls be x days
time taken by boys be y days
work done by 1 girl in one day=1/x
work done by 1 boy in one day=1/y
8/x+12/y = 1/10....eq 1
6/x+ 8/y = 1/14.....eq2
Let u=1/x & v=1/y
8u+ 12y=1/10..eq3
6u+8v= 1/14...eq4
Multiplying eq3 by 2 & eq4 by 3
16u+ 24y=2/10....eq5
18u+24v= 3/14.....eq6
subtract eq 5 & 6
-2u= -3/14+2/10
-2u = (-3×10 +2×14)/140
-2u=( -30+28)/140
-2u=-2/140
u=1/140
put this value in eq 5
16u+ 24y=2/10
16×1/140 +24y =1/5
4/35+24y= 1/5
24y= 1/5-4/35
24y= (1×7 -4)/35
24y = (7-4)/35
24y= 3/35
y= 3/35×24
y= 1/280
u=1/x
1/140 = 1/x
x=140
v=1/y
1/280 = 1/y
y=280
A girl complete the work in 140 days
A boy can complete the work in 280 days
time taken by boys be y days
work done by 1 girl in one day=1/x
work done by 1 boy in one day=1/y
8/x+12/y = 1/10....eq 1
6/x+ 8/y = 1/14.....eq2
Let u=1/x & v=1/y
8u+ 12y=1/10..eq3
6u+8v= 1/14...eq4
Multiplying eq3 by 2 & eq4 by 3
16u+ 24y=2/10....eq5
18u+24v= 3/14.....eq6
subtract eq 5 & 6
-2u= -3/14+2/10
-2u = (-3×10 +2×14)/140
-2u=( -30+28)/140
-2u=-2/140
u=1/140
put this value in eq 5
16u+ 24y=2/10
16×1/140 +24y =1/5
4/35+24y= 1/5
24y= 1/5-4/35
24y= (1×7 -4)/35
24y = (7-4)/35
24y= 3/35
y= 3/35×24
y= 1/280
u=1/x
1/140 = 1/x
x=140
v=1/y
1/280 = 1/y
y=280
A girl complete the work in 140 days
A boy can complete the work in 280 days
Community Answer
8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 b...
Calculating the time taken by one girl and one boy to finish the work:
Given:
- 8 girls + 12 boys can finish the work in 10 days
- 6 girls + 8 boys can finish the work in 14 days
Step 1: Finding the work done by each girl and each boy in one day:
- Let the work done by one girl in one day be G and work done by one boy in one day be B
- From the first scenario: 8G + 12B = 1/10 (as they finish the work in 10 days)
- From the second scenario: 6G + 8B = 1/14 (as they finish the work in 14 days)
Step 2: Solving the equations:
- Multiply the first scenario by 3 and the second scenario by 4 to make the coefficients of G equal
- We get: 24G + 36B = 3/10 and 24G + 32B = 1/14
- Subtract the second equation from the first: 4B = 2/35
- Therefore, B = 1/70 (work done by one boy in one day)
Step 3: Calculating the time taken by one girl:
- Substitute the value of B in the first scenario equation: 8G + 12(1/70) = 1/10
- Simplify to get: 8G + 12/70 = 1/10
- 8G = 1/10 - 12/70 = 7/70
- G = 7/560 = 1/80 (work done by one girl in one day)
Conclusion:
- One girl alone can finish the work in 80 days
- One boy alone can finish the work in 70 days
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8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work?
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8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work?.
8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 8 girls and 12 boys can finish a work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work?.
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