Question

if hemanth works for 20 days and manoj, work for 15 days then 3/5th work has been completed. if manoj works for 60 days and hemanth works for 16 days then 2/5 of the work has been completed. find in how many days both can completed the work together
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Answer 1

Both can completed the work together in "30 days".

Step-by-step explanation:

Let efficiency of Hemant = h units/day and

Efficiency of Hemant = m units/day

According to question,

$\dfrac{20 h + 15 m}{6 m + 16 h}$ = $\dfrac{3}{2}$

⇒ 40 h + 30 m = 18 m + 48 h

⇒ 30 m  - 18 m  = 48 h - 40 h

⇒ 12 m  = 8 h

∴ $\dfrac{h}{m}$ = $\dfrac{3}{2}$

Let h = 3x and  m = 2x

∴ Total work = $\frac{30(3x) + 15(2x) }{3}$ × 5 = 150x

∴ Required time = $\dfrac{150x}{5x}$ = 30 days

Hence, both can completed the work together in 30 days.

Answer 2

Both the Hemanth and Manoj can completed the work together for 30 days.

Given:

If hemanth works for 20 days and manoj, work for 15 days then 3/5th work has been completed.

If manoj works for 60 days and hemanth works for 16 days then 2/5 of the work has been completed.  

To find:

Find in how many days both can completed the work together

Solution:

Let the efficiency of hemanth be 'a' and manoj be 'b'

Therefore,

$20a + 15b = \frac{3}{5}$

$60a + 16b = \frac{2}{5}$

Dividing there equations, we get

$\frac{20 a+15 b}{16 a+6 b}=\frac{3}{2}$

40a + 30b = 48a + 18b

8a = 12b

$\frac{a}{b} = \frac{3}{2}$

let a = 3x, b = 2x

Total work = $\frac{(20 \times 3x + 15 \times 2x)}{3 \times 5} = 150x$

Time required = $\frac{150x}{5x}$ = 30 days

Result:

Both the Hemanth and Manoj can completed the work together for 30 days.

To know more:

Mohan takes 16 days less than manoj to do a piece of work . Both working together will finish it in 15 days .How many days will manoj alone take to finish the work

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