TIME AND WORK tips, tricks and shortcut Continued..

TIME AND WORK Continued.....

Today we will look at some hard type of problems in time and work.

EG 1— If 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days??

SOLUTION

Given,

              12 men è4 days to complete whole work

              15 women è4 days to complete whole work

              To complete work,

 6 men worked è 2days and left

?? women required è 3 days to complete REMAINING work

Now,

              12 men è4 days

              15 women è4 days

Therefore,

              1man è 12*4 = 48m

              1woman è 15*4 = 60w

So,

              48m = 60w

i.e          4m = 5w   --(i)

NOTE :-- We need to understand that how much work was completed and how is remaining.

So,

              6 men completed SOME work in 2 days

We will find out this SOME WORK first.

              6 men è 2 days

i.e          6*2 = 12m work was completed (out of 48m work).

Therefore,

              48m – 12m

              = 36m work is REMAINING (out of 48m work).

Now,

              4m = 5w  ---from (i)

i.e          36m = 45w

So we can also say 45w work is remaining out of 60w work.

We need,

              ?? women è 3 days to complete 45w work

i.e          ?? women = 45 / 3

                                    = 15 days

EG 2 - P, Q and R begin to finish a work together. P is twice as efficient as Q and R is 2/3rd as efficient as Q. P leaves after 2 days while Q leaves after 4 days. How many days will R further take to finish off the work, if Q alone can finish the work in 16 days??

SHORTCUT

Given,

              P = 2Q (P is twice as efficient as Q)

R = 2/3 * Q (R is two-third as efficient as Q)

Q è 16 days to complete work alone

P leaves after 2 days and

Q leaves after 4 days.

Now,

              P = 2Q            therefore P takes ½ time compared to Q

              R = 2/3 *Q    therefore R takes 3/2 time compared to Q

[TIME is inversely proportional to EFFICIENCY]

Also,

              Q è 16 days alone   ---(Given)

Therefore,

              P è 16 * ½    è 8 days alone and

              R è 16 * 3/2 è 24 days alone

Now just think don’t write anything,

                             P è 8 days to completes whole i.e 100% work

                             P è 2 days to completes 25% work

Similarly,

Q è 16 days to completes whole i.e 100% work

              Q è 4 days to completes 25% work

Therefore total work completed by P and Q is, 25% + 25% = 50%

 SO, 50% more is REMAINING.

Which R has to complete.

              R è 24 days to completes whole i.e 100% work

R è 12 days to completes REMAINING 50% work

[12 days are 50% of 24 days.]

Out of 12 days R has worked for 4 days with P and Q.

Hence,

              12 -4 = 8 days