A takes twice as much time as B and thrice as much as C to complete a

1.	A takes twice as much time as B and thrice as much as C to complete a piece of work. They together complete the work in 1 day. In what time will A alone complete the work?1. 6 days.2. 2 days.3. 3 days.4. 5 days
Answer» Correct Answer - Option 1 : 6 days. Given: A’s time = 2 × time taken by B = 3 × time taken by C And together they complete work in 1 day Concept used: Days is inversely proportional to efficiency If A does a work in x days and B does a work in y days, the ratio of days = x : y and The ratio of efficiency = y : x If a person does a work in ‘n’ days then one day work by a person will be 1/n part of total work Calculation: A’s time = 2 × taken by B ⇒ A’s time/B’s time = 2/1 ----(i) A’s time = 3 × time taken by C ⇒ A’s time/ time taken C = 3/1 ----(ii) After multiplying equation(i) by 3 and equation (ii) by 2 we get, Ratio of time is ⇒ A : B : C = 6 : 2 : 3 And Efficiency ratio = (1/6) : (1/2) : (1/3) ⇒ Efficiency ratio = 1 : 3 : 2 Total work = sum of efficiency × days ⇒ (1 + 3 + 2) × 1 ⇒ 6 × 1 ⇒ 6 A alone can complete the work in= total work/ efficiency of A ⇒ 6/1 ⇒ 6 days. ∴ A can alone complete the work in 6 days.

A takes twice as much time as B and thrice as much as C to complete a piece of work. They together complete the work in 1 day. In what time will A alone complete the work?1. 6 days.2. 2 days.3. 3 days.4. 5 days

Answer» Correct Answer - Option 1 : 6 days.

Given:

A’s time = 2 × time taken by B = 3 × time taken by C

And together they complete work in 1 day

Concept used:

Days is inversely proportional to efficiency

If A does a work in x days and B does a work in y days, the ratio of days = x : y and

The ratio of efficiency = y : x

If a person does a work in ‘n’ days then one day work by a person will be 1/n part of total work

Calculation:

A’s time = 2 × taken by B

⇒ A’s time/B’s time = 2/1 ----(i)

A’s time = 3 × time taken by C

⇒ A’s time/ time taken C = 3/1 ----(ii)

After multiplying equation(i) by 3 and equation (ii) by 2 we get, Ratio of time is

⇒ A : B : C = 6 : 2 : 3

And Efficiency ratio = (1/6) : (1/2) : (1/3)

⇒ Efficiency ratio = 1 : 3 : 2

Total work = sum of efficiency × days

⇒ (1 + 3 + 2) × 1

⇒ 6 × 1

⇒ 6

A alone can complete the work in= total work/ efficiency of A

⇒ 6/1

⇒ 6 days.

∴ A can alone complete the work in 6 days.