Question

7. Work done by A in one day is
four times the work done by B
in one day, while the work
done by B in one day is one-
third of the work done by C in
one day. C alone can complete
the work in 16 days. In how
many days can all the three
together complete the work?​

Answer 1

AnswEr:

They together can complete the work in 6 Days.

Given:

• Work Done by A is Four Times the work Done by B.

So, A = 4B

• Work Done by B is One third the work Done by C.

So, C = 3B

A : B = 4 : 1 & B : C = 1 : 3

$\rule{200}2$

C can complete the work in 16 Days. [Given]

Ratio of work of A,B & C in 1 day.

A: B: C = 4: 1 :3

Work Done by C in 16 Days

= 3 × 16

= 48

Now, Time Taken by All three (A,B & C) to complete the work

$:\implies\sf\: \dfrac{4 + 1 + 3}{48}$

$:\implies\sf\: \dfrac{8}{48}$

$:\implies\sf\: \bold{6 \: Days}$

Hence, All three can complete work together in 6 days.

Answer 2

Given :-

• A = 4B
• B = (1/3)C
• C Alone can complete The work in = 16 days.

To Find :-

• In How Many days all three can complete whole work.

Solution :-

→ A = 4B

→ (A/B) = (4/1)

So ,

→ Efficiency of A = 4 unit / day.

→ Efficiency or B = 1 unit / day.

______________________

→ B = (1/3)C

→ (B/C) = (1/3)

So ,

→ Efficiency of B = 1 unit / day.

→ Efficiency or C = 3 unit / day.

_________________

Now,

→ A : B = 4 : 1

→ B : C = 1 : 3

So ,

→ A : B : C = (4*1) : (1 *1) : (1 * 3) = 4 : 1 : 3. = Efficiency of A , B & C.

_________________

Now,

→ C per day work = Efficiency of C = 3 unit /day.

→ So, Total work = 16 * 3 = 48 units.

→ And, Efficiency of All Together = 4 + 1 + 3 = 8 unit/day.

Hence ,

→ Time They will Take Together = (Total work) / (Total Efficiency) = (48/8) = 6 Days..(Ans).

Hence , all the three together complete the work in 6 days.