9. Two persons A and B together can do a piece of work in 10 days, persons B and C togethercan do it in 15 days, persons C and A together can do it in 12 days. How long will they take to finish the work, working altogether? How long would each take to do the same work?
Answers
Given:-
- (A + B) can do a work = 10 days
- (B + C) can do a work = 15 days
- (A + C) can do a work = 12 days
To Find :-
- work finish by (A + B + C)= ? days
- work finish separately by them = ? days
Solution :-
We will solve this question by setting up equation as per the given clue in the question. As given in the question that two persons A and B together can do a piece of work in 10 days, persons B and C togethercan do it in 15 days, persons C and A together can do it in 12 days. Let assume their one days work be 1/x in the form of fraction.
Calculation begin :-
➞ Work finish by ( A + B + C) = Sum of their 1 day's work
➞ (A +B) + (B + C) + (A + C)= 1/10 + 1/15 + 1/12
➞ 2A + 2B + 2C = 6 + 4 + 5/60
➞ 2(A + B + C) = 15/60
➞ 2(A + B + C) = 1/4
➞ (A + B + C) = 1/4×2 = 1/8
- Now calculate work done by A , B , C alone:-
➞ A + B = 1/10 ---------(i)
➞ B + C = 1/15 ---------(ii)
➞ A + C = 1/12 --------(iii)
- Substracting equation ( ii) and (iii) :-
➞ B + C = 1/15
➞ A + C = 1/12
- By Solving we get here :-
➞ B - A = 1/15 - 1/12
➞ B - A = 4 - 5/60
➞ B - A = -1/60------(iv)
- From equation (i) and (vi)
➞ A + B = 1/10
➞ B - A = -1/60
- By adding we get here :-
➞ 2B = 1/10 - 1/60
➞ 2B = 6 - 1/60
➞ B = 5/60 × 2 = 1/24
- Putting the value of B in eq (ii)
➞ B + C = 1/15
➞ 1/24 + C = 1/15
➞ C = 1/15 - 1/24
➞ C = 8 - 5/120
➞ C = 3/120 = 1/40
- Putting the value of C in eq (iii)
➞ A + C = 1/12
➞ A + 1/40 = 1/12
➞ A = 1/12 - 1/40
➞ A = 10 - 3/120
➞ A = 7/120
➞ A = 1/17
Hence ,
- (A + B + C ) finished the work = 8 days
- A finished the work = 17 days
- B finished the work = 24 days
- C finished the work = 40 days
Given :-
Two persons A and B together can do a piece of work in 10 days, persons B and C togethercan do it in 15 days, persons C and A together can do it in 12 days
To Find :-
How long will they take to finish the work, working altogether? How long would each take to do the same work?
Solution :-
We have
A + B = 10 days
B + C = 15 days
C + A = 12 days
They all are repeating 2 times
2(A + B + C) = 1/10 + 1/15 + 1/12
2(A + B + C) = 6 + 4 + 5/60
2(A + B + C) = 15/60
2(A + B + C) = 1/4
A + B + C = 1/4 × 2
A + B + C = 1/8
Now
A + B = 1/10
B + C = 1/15
C + A = 1/12
Subtract 2 and 3
(B + C) - (C + A) = 1/15 - 1/12
B + C - C - A = 4 - 5/60
B - A = -1/60
Now
B - A - A + B = 1/15 - 1/60
2B = 4 - 1/60
2B = 3/60
2B = 1/20
B = 1/20 × 2 = 2/20
B = 1/10
B = 10 days
Now
B + C = 1/15
1/10 + C = 1/15
C = 1/10 - 1/15
C = 3 - 2/30
C = 1/30
C = 30 days
Again
A + C = 1/12
A + 1/30 = 1/12
A = 1/12 - 1/30
A = 5 - 2/60
A = 3/60
A = 1/20
A = 20 days[tex][/tex]