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Sita and Rita can do a piece of work in 10 days and 20 days, respectively. They fell ill and Sita was able to perform the task with half of her previous efficiency while Rita was able to perform the task with 40% of her previous efficiency only. How many days will they take to finish the task together being ill?

Sita and Rita can do a piece of work in 10 days and 20 days, respectively. They fell ill and Sita was able to perform the task with half of her previous efficiency while Rita was able to perform the task with 40% of her previous efficiency only. How many days will they take to finish the task together being ill? Correct Answer 100/7

Sita and Rita can do a piece of work in 10 days and 20 days, respectively.

CONCEPT:

Basic efficiency concept:

FORMULA USED:

Efficiency × Time = Total work

CALCULATION:

We have,

Efficiency of Sita before falling ill = 1/10 units/day

⇒ Efficiency of Sita after falling ill = (1/2) × (1/10) = 1/20 units/day

And

Efficiency of Rita before falling ill = 1/20 units/day

⇒ Efficiency of Rita after falling ill = 0.4 × (1/20) = 1/50 units/day

Let d be the number of days to complete the task together after they both fell ill

We have,

(1/20 + 1/50) × d = 1

⇒ 7d/100 = 1

⇒ d = 100/7 days

∴ They take 100/7 days to finish the task together being ill.

Shortcut Trick:

⇒ Efficiency of Sita = 20/10 = 2 units/day

⇒ Efficiency of Rita = 20/20 = 1 units/day

Now, after getting ill:

Efficiency of Sita = 2 × 0.5 = 1 units/day

Efficiency of Rita = 1 × 0.4 = 0.4 units/day

Suppose they take ‘x’ days to finish the work:

(1 + 0.4) × x = 20

⇒ x = 20/1.4 = 100/7

∴ They take 100/7 days to finish the task together being ill.

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