Question

Dinesh and dipu can design an application software in 16 hours and 12 hours respectively. Dinesh joins dipu 4 hours before completing the design, dipu had started the design work alone. Find how many days dipu has worked alone?

Answer 1

Answer:

Dipu has work  $\frac{5}{24}\hspace days$ alone

Step-by-step explanation:

Dinesh can design an application software in 16 hours

Thus, Dinesh's 1 hour work $=\frac{1}{16}$

Also, Dipu can design an application software in 12 hours

Thus, Dipu's 1 hour work $=\frac{1}{12}$

Total work to design an application software is LCM of 12 and 16 $=48\hspace{0.1cm}parts$

Now, Dinesh can complete work in 1 hour $= \frac{48}{16}=3\hspace{0.1cm}parts$

Dipu can complete work in 1 hour $= \frac{48}{12}=4\hspace{0.1cm}parts$

Given that Dinesh joins Dipu in last 4 hours of work

Work done by (Dinesh + Dipu) in 1 hours $= 3 + 4 = 7\hspace{0.1cm}parts$

Work done by (Dinesh + Dipu) in 4 hours $= 4 \times 7 = 28\hspace{0.1cm}parts$

Work Remaining $= 48 - 28 = 20\hspace{0.1cm}parts$

Now, 20 parts of work is done by Dipu alone

4 parts of work done by Dipu in 1 hour

20 parts of work done by Dipu in $\frac{20}{4} = 5\hspace{0.1cm}hours = \frac{5}{24}\hspace days$

Hence, Dipu has work  $\frac{5}{24}\hspace days$ alone