# At their usual efficiency levels, A and B together - Quantitative Aptitude – Arithmetic | Time and work |

## CAT 2019 – Slot 1 - Time and work- Question 3 - At their usual efficiency levels, A and B together

Q. 3: At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

1. 18

2. 12

3. 36

4. 24

let usual efficiency of A = 2a and that of B = b

So total work = 12*(2a+b) = 24a+12b————1)

In 2nd case when efficiency of A is halved and efficiency of B get tripled , new efficiency of A = 2a/2 = a

New efficiency of B = b*3 =3b

Total work = 9(a+3b) = 9a+27b ——————-2)

From eq 1) and 2)

24a+12b = 9a + 27b

15a = 15b

Or a=b

So total work = 24a+12b = 24a+12a = 36a

Time taken by A alone to complete the work = 36a/2a = 18 days

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