Question

please answer this difficult question.....n​

Answer 1

Answer:

It is given that P and Q can do a piece of work in 12 days and 15 days respectively, if they are doing it alone. Now we are asked to find how many days it would take for the work to be done if P worked for 3 days alone and Q joins on after.

Analyzing the information given we get,

→ P = 12 days

→ Part of work done in 1 day = 1/12 th of the work

→ Q = 15 days

→ Part of work done in 1 day = 1/15 th of the work

So it is given that P worked for 3 days.

→ Part of work done by P in 3 days = 3/12 = 1/4th of the work.

Remaining work after P works for 3 days is = 1 - 1/4 = 3/4 = 0.75

Also it is given that Q joins after 3 days and works together.

→ Part of work done by P and Q in 1 day is = 1/12 + 1/15 = 27/180 = 3/20

Therefore in 1 day part of work done by P and Q is 3/20 = 0.15

So in 1 day they can do 0.15 of the work. Hence in how many days will they be able to do 0.75 ?

Applying the concept of Ratio and Proportion we get,

→ 1 day : 0.15 :: x days : 0.75

→ 0.75 × 1 = 0.15 × x

→ x = 0.75 / 0.15

→ x = 5 days

Therefore the work was completed within 5 days after Q joined. Therefore total number of days it took to complete the work is 5 + 3 = 8 days

Answer 2

Question:

P and Q can do a piece of work in 12 days and 15 day respectively. P started the work alone and then, after 3 days Q joined with him till the work was completed. How long did the work last?

⇒ The work lasted for $5\frac{7}{19} days$

Explanation:

It is stated that,

P alone can do the work in 12 days.

∴ In 1 day P can do (1/12) part of the work.

∴ In 3 days P can do (1×3/12)

                                    = 1/4 part of the work.

∴ After P working for 3 days alone, the part of the work left _

1-(1/4)

= (4-1)/4 [∵ The L.C.M. of the denominators is 4.]

= 3/4 part of the work.

∴ P and Q together did 3/4 part of the work.

Q alone can do the work in 15 days.

∴ In 1 day Q alone can do (1/15) part of the work.

∴ In 1 day P and Q together can do_

(1/4) + (1/15)

=(15+4)/60 [∵ The L.C.M. of the denominators is 60.]

= 19/60 part of the work.

Hence,

19/60 part of the work P and Q together can do in 1 day.

∴ 1 part of the work P and Q together can day in (60/19) days.

∴ 3/4 part of the work P and Q together can do in_

(60×3)/(19×4)

=(15×3)/19

= 45/19

= $2\frac{7}{19\\}$ days.

∴ P and Q together do the remaining part of the work in $2\frac{7}{19}$ days.

P worked alone for 3 days.

∴ The work lasted after _

$3+2\frac{7}{19} \\= 3 +\frac{45}{19} \\=\frac{57+45}{19} \\= \frac{102}{19} \\=5\frac{7}{19} days$

[∵ The L.C.M. of the denominators is 19.]

∴ The work lasted for $5\frac{7}{19}$  days.