In this chapter , we will study the relationship among the quantity of work given , wages given to them stipulated time , number of persons , etc , and after it , we will be able to complete the work in stipulated time by arranging some persons according to the work but before it , we should have known some basic rules.
IMPORTANT RULES FOR TIME AND WORK :
RULE 1:
If a person can do a piece of work in 'n' days, then he will do 1/n of the work in one day and if a person can do 1/n th of work in one day , then he will Complete the work in n days.
RULE 2:
If A and B can do a piece of work in x days and y days respectively . Then time taken by (A + B) to complete the work is equal to reciprocal of (A + B)'s one days's work.
or
If A and B can do a piece of work in x days and y days respectively, then time taken to complete the work is (x*y) / (x + y) days
If A and B can do a piece of work in x days . B and C can do same work in y days , C and A can do same work in z days . Then , they will complete the same work in 2xy / (xy + yz + zx) days by working together.
RULE 3:
If two groups, M1 persons of the first group can do W1 work in D1 days working T1 h in a day and M2 persons of second group can do W2 work in D2 days working T2 h in a day . If each person of both group has the same efficiency of work, then
M1*D1*T1*W2 = M2*D2*T2*W1
RULE 4:
If m men or n women can do a piece of work in a days then x men and y women can do the same work in [1 / (x / (m*a)) + (y / (n*a))]
RULE 5:
If A can do a work in x days and B can do y% fast than A, then B will compete the work in 100*x / (100 + y)
RULE 6:
If A,B and C can do a piece of work in x,y and z days respectively and they received rs k as wages by working together then
share of A = [yz / (xy + yz + zx)] * k
share of B = [xz / (xy + yz + zx)] * k
share of C = [xy / (xy + yz + zk)] * k
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- If A and B can do a piece of work in x and y days , A and B started working together but A left the work t days before complete the work then time taken to complete the work will be (x + t)*y / (x + y) days and if B left the work t days before complete the work will be (y + t)*x / (x + y) days.
- If there is ratio for a days x men at a compound after B days y men also joined them or y men left them , then remaining work will be sufficient for (a - b)*x / (x ± y ) days for (x ± y) men
- If A and B can do a piece of work in x and y days , respectively. They start working together and after t days A leaves the work then time taken to finish the work will be x * (y - t) / y days.
Lets do some exercises related to time and work,
| time and work 1 |
| time and work 2 |
| time and work 3 |
| solutions 1 |
| solutions 2 |
| solutions 3 |
| solutions 4 |
THANKS FOR READING THIS AT Math Capsule
