Question

Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours how how long will it take to do it working together

Answer 1

Given that Ravi can do a piece of work in 15hours while Raman can do it in 12 hours .then how long will it take to do it by working together.

let the total work be 1 .

Ravi's 1 hours' work = 1 /15 units

Raman's 1 hours' work = 1 /12 units

Ravi's and Raman's 1 hours work

=( 1 /15 ) + ( 1 /12 )

=(12 + 15) / ( 5 × 12 )

=27 / 180 = 3 /20 units

=1/6.67 units

therefore , if they worked together then they will finish the work in

6.67h = 6 hr 40min .

Answer : 6 hr 40 min .
_______________________________

Answer 2

Ravi can do a piece of work in 15 hours

⇒ 1 hour = 1/15 of the work

Raman can do a piece of work in 12 hours

⇒ 1 hour = 1/12 of the work

Find the amount of work done in 1 hour if they do the work together:

1 hour = 1/15 + 1/12 = 3/20 of the work

Find the number of hours needed to complete the work:

3/20 of the work = 1 hour

1/20 of the work = 1 ÷ 3 = 1/3

20/20 of the work = 1/3 x 20 = 20/3 = 6 2/3 hours  ≈ 6 hours 40 mins

Answer: They can complete the work in 6 hours 40 mins if the do it together.

------------------------------------------------------------------------------------------------------------------

SHORTCUT METHOD:

$\text {Number of hours = } \dfrac{12 \times 15}{12 + 15}= \dfrac{20}{3}= 6.67= \text { 6 hours 40 mins}$