### TIME AND WORK math capsule

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**n 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 :

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__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.

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__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.

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__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

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__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))]

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__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)

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__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 |

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