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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: A can do 40% of a work in 6 days and B can do 30% of the same work in 3 days. They started the work together but B left after 2 days and A continued to work. In how many days was the entire work completed? Quantity B: Type 1 workers are two-and-a-half times as efficient as Type 2 workers. If 12 Type 1 workers can complete a task in 10 days, how many days would it take 6 type 1 and 10 type 2 workers to complete the same task?

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: A can do 40% of a work in 6 days and B can do 30% of the same work in 3 days. They started the work together but B left after 2 days and A continued to work. In how many days was the entire work completed? Quantity B: Type 1 workers are two-and-a-half times as efficient as Type 2 workers. If 12 Type 1 workers can complete a task in 10 days, how many days would it take 6 type 1 and 10 type 2 workers to complete the same task? Correct Answer Quantity A = Quantity B or No relation

Quantity A: 

A can do 40% of a work in 6 days

∴ A can do 100% of the work in 15 days

B can do 30% of the same work in 3 days

∴ B can do 100% of the same work in 10 days

Total work = LCM of (15 and 10) = 30

Efficiency of A = 30/15 = 2

Efficiency of B = 30/10 = 3

Work done by A and B together in 2 days = 5 × 2 = 10

Remaining work = 30 – 10 = 20

Remaining work done by A = 20/2 = 10 days

∴ Total Number of days = 10 + 2 = 12 days

Quantity B: 

Let the efficiency of type 2 workers be 2x

Efficiency of type 1 workers = 2x × (5/2) = 5x

As we know,

Total work = total work

Let 6 type 1 and 10 type 2 workers complete the work in y days, then

No. of type 1 workers × Efficiency of type 1 worker × days = (No. of type 1 workers × efficiency of type 1 worker × days) + (No. of type 2 workers × efficiency of type 2 worker × days)

⇒ 12 × 5x × 10 = 6 × 5x × y + 10 × 2x × y

⇒ 600x = 30xy + 20xy

⇒ 600x = 50xy

⇒ y = 600x/50x

⇒ y = 12 days

∴ Quantity A = Quantity B or No relation

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