# CLASS-10QUADRATIC EQUATIONS - PROBLEM ON TIME & WORK

Problem On Time & Work

Example.1) A can do a piece of work in x days and B can do it in (x + 16) days. If both working together can do it in 15 days, calculate x.

1                                     1

Ans.) A’s 1 day’s work = -------- and B’s 1 day’s work = -----------

x                                  (x + 16)

1              1

(A + B)’s 1 day’s work = [ -------- + ----------]

x           (x + 16)

But, it is being given that both working together can do the work in 15 days

1

So, (A + B)’s 1 day’s work = -------

15

1              1              1

So, [-------- + ----------] = -------

x          (x + 16)          15

(x + 16) + x           1

=> [---------------] = -------

x (x + 16)             15

=> 15 (2x + 16) = x² + 16x

=> 30x + 240 = x² + 16x

=> x² + 16x – 30x – 240 = 0

=> x² - 14x - 240 = 0

=> x² - (24 – 10)x – 240 = 0

=> x² - 24x + 10x – 240 = 0

=> x (x – 24) + 10 (x – 24) = 0

=> (x – 24)(x + 10) = 0

=> (x – 24) = 0 or (x + 10) = 0

=> x = 24 or x = - 10

=> x = 24           [x ≠ - 10, since number of days cannot be negative]

So, the required working days is 24       (Ans.)

Example.2) One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill it in 6 hours 40 minutes. Find the time that each pipe will take to fill the cistern.

Ans.) Let the pipes A & B take x hrs. and (x + 3) hrs. respectively to fill the cistern.

1

Part of the cistern filled by A in 1 hr = -------

x

1

Part of the cistern filled by B in 1 hr = ---------

(x + 3)

1             1

Part of the cistern filled by (A + B) in 1 hr = [------- + ---------]

x          (x + 3)

Total time taken by both to fill the cistern = 6 hours 40 minutes

40

= 6 --------

60

2           20

= 6 ------ = -------- hrs.

3           3

1            3

Part of the cistern filled by both in 1 hour = -------- = -------

20/3         20

So, as per the given condition –

1              1               3

--------- + ---------- = --------

x            (x + 3)          20

x + 3 + x            3

=> -------------- = -------

x (x + 3)            20

=> 20 (2x + 3) = 3 (x² + 3x)

=> 40x + 60 = 3x² + 9x

=> 3x² + 9x – 40x – 60 = 0

=> 3x² - 31x – 60 = 0

=> 3x² - (36 – 5)x – 60 = 0

=> 3x² - 36x + 5x – 60 = 0

=> 3x (x – 12) + 5 (x – 12) = 0

=> (x – 12) (3x + 5) = 0

=> (x – 12) = 0 or (3x + 5) = 0

=> x = 12 or x = - 5/3

=> x = 12             [ x ≠ - 5/3, since time cannot be negative]

Hence, the first pipe alone takes 12 hours to fill the cistern, while second alone takes (x + 3) = (12 + 3) = 15 hours to fill it.     (Ans.)