# Quantitative Aptitude – Arithmetic – Time and work

## Slot – 1 – Quantitative Aptitude – Arithmetic – Time and work – At their usual efficiency levels, A and B together

Q. 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

Solution: 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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