Symbiosis National Aptitude Test SNAP 2013 Paper

Question : 10 of 150

Marks: +1, -0

A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone ?

2 : 5
2 : 7
3 : 7
1 : 5

Validate

Solution:

A +B 1 day’s work =

1/{20}

... (i)
B + C 1 day's work =

1/{30}

... (ii)
C + A 1 day's work =

1/{40}

... (iii)
Adding eqs. (i), (ii) and (iii)
2 (A + B + C) =

1/{20}+1/{30}+1/{40}

2 (A + B + C) =

{6+4+3}/{120}

⇒ A + B + C 1 day work together =

{13}/{240}

A’ Alone 1 day’s work
= (A + B + C) 12 day’s work – (B + C) 1 day’s work
A =

{13}/{240}-1/{30}

⇒

{13-8}/{240}

5/{240}

Number of days taken by A =

{240}/5

days
C ’ Alone 1 day’s work
= (A + B + C) 12 day’s work – (A + B) 1’ day’s work
⇒

{13}/{240}-1/{20}

⇒

{13-12}/{240}

1/{240}

Number of days taken by C =

{240}/1

days
Required Ratio

{240}/5:{240}/1

⇒ 1 : 5

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