Skip to main content

Time and Work

If A can do a piece of work in n days, then A's 1 day's work = 1/n 
If A and B work together for n days, then (A+B)'s 1 days's work = 1/n 
If A is twice as good workman as B, then ratio of work done by A and B = 2:1
 Basic Formula :
If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then 
M1 D1 H1 / W1 = M2 D2 H2 / W2 
If A can do a piece of work in p days and B can do the same in q days, 
A and B together can finish it in pq / (p+q) days.

Illustration 1:  Samir can do a job in 30 days. In how many days can he complete 70% of the job?
Sol: Now as per the question he finishes the work in 30 days, or he can do 100% of the work in 30 days. If he has to do only 70% of the work, he will require 70% of the time.
 Number of days required = 30 × 70/100 = 21 days.
Illustration 2:  Reshma can do 75% job in 45 days. In how many days can she complete the job?
Sol: Every work is 100% in itself. Reshma does 75% of the work in 45 days. That means she does 1% of the work in 45/75 days and she will do 100% of the work in 100 × 45/75 = 60 days.
Illustration 3: John can do a piece of work in 60 days; he will do how much of the work in 40 days?
Sol: In 1 day, John does 1/60th of the work, so in 40 days he will do 40 × 1/60 = 2/3rd of the work.
Illustration 4: Anup can finish a piece of work in 30 days. He will finish what percent of the work in 15 days?
Sol: In 1 day, he does 1/30th of the work, and in 15 days, he will do 15/30th of the work which is 100 × 15/30 = 50%.
Illustration 5: Ria can do a piece of work in 40 days, she will take how many days to finish three-fourth of the work?
Sol:  Ria can complete the work in 40 days.  She will do ¾th of the work in ¾th of the total time. i.e. she will need 40 × 3/4 = 30 days.

Comments

Post a Comment

Popular posts from this blog

Profit and loss

Formulae:- Gain = Selling Price(S.P.) - Cost Price(C.P)  Loss = Cost Price (C.P.) - Selling Price (S.P) Gain % = Gain x 100 / C.P. Loss % = Loss x 100 / C.P  S.P. = [(100 + Gain%)/100] x C.P  S.P. = [(100 - Loss%)/100] x C.P  C.P. = [100/ (100 + Gain%) ] x S.P  C.P. = [100/ (100 - Loss%) ] x S.P  When a person sell two similar items , one at a gain of say x% , and other at a loss of x% then the seller always incure a loss given by - Loss % = ( Common loss & gain % / 10 )2  If a trader professes to sell his goods at cost price , but uses false weight , then Gain% = [ Error / (True value – Error ) ] x 100 % TRUE DISCOUNT  Ex. Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum.  Clearly, Rs. 100 at 14% will amount to R. 156 in 4 years. So, the payment of Rs. now will clear off the debt of Rs. 156 due 4 years hence. We say that: Sum due = Rs. 156 due 4 years  hence: Present Worth (P.W.) = Rs. 100;...
Post a Comment
Read more

LCM and HCF

Greatest Common Divisor (GCD)/ Highest Common Factor (HCF) The highest common factor of two or more numbers is the greatest common divisor, which divides each of those numbers an exact number of times. The process to find the HCF is Express the numbers given as a product of prime numbers separately i.e. finds factors of numbers Take the product of prime numbers common to both numbers Illustration 1: Find the HCF of 1728 and 14. Sol: The prime factorization of 1728 is 12 × 12× 12= 3 3 x2 6 . The prime factorization of 14 is 2 × 7. The common prime factor is 2. HCF = 2. Illustration 2: Find the HCF of 27, 18 and 36. Sol: Firstly find the prime factors of the numbers such as 27 = 3 × 3 × 3, 18 = 3 × 3 × 2 and 36 = 3 × 3 × 2 × 2, then take the common prime numbers, which are 3 & 3. Now the product of these prime numbers i.e. 3 × 3 = 9 is the HCF of these two numbers. Understanding LCM or Least Common Multiple The least common multiple (LCM) of two or more numbers is the smallest of the...
Post a Comment
Read more