Previous Year Questions

Let time taken by A, B, and C alone to finish the work working with their original efficiencies is 'a' days, '15b' days, and '3c' days respectively.

Time taken by A alone when working with 50% of original efficiency = a * (100/50) = 2a days

Time taken by B alone when working with 15/8^th of original efficiency = 15b * (8/15) = 8b days

Time taken by C alone when working with 60% of original efficiency = 3c * (100/60) = 5c days

According to the question:

(1/2a) + (1/8b) + (1/5c) = (1/10) ........ (1)

From I:

Ratio of original efficiency of A to B = 3: 4

Ratio of time taken by A and B = 4: 3 = a: 15b

a = 20b ......... (2)

Statement I alone is not sufficient.

From II:

(1/15b) + (1/3c) = (3/40) ......... (3)

Statement II alone is not sufficient.

From III:

a - 3c = 16 ....... (4)

Statement III alone is not sufficient.

From I and II:

From equations (1), (2) and (3):

(1/40b) + (1/8b) + (1/5c) = (1/10)

(3/20b) + (1/5c) = (1/10)

(1/15b) + (1/3c) = (3/40)

b = 2, c = 8 and a = 40

Time taken by all of them to finish the work when working with their original efficiencies = 1/[(40) + (1/30) + (1/24)] = 120/(3 + 4 + 5) = 10 days

Statements I and II together are sufficient.

From I and III:

From equations (1), (2) and (4):

(1/40b) + (1/8b) + (1/5c) = (1/10)

(3/20b) + (1/5c) = (1/10)

a - 3c = 16

20b - 3c = 16

b = 2, c = 8 and a = 40

Time taken by all of them to finish the work when working with their original efficiencies = 1/[(40) + (1/30) + (1/24)] = 120/(3 + 4 + 5) = 10 days

Statements I and III together are sufficient.

From II and III:

From equations (1), (3) and (4):

(1/2a) + (1/8b) + (1/5c) = (1/10)

(1/15b) + (1/3c) = (3/40)

a - 3c = 16

b = 2, c = 8 and a = 40

Time taken by all of them to finish the work when working with their original efficiencies = 1/[(40) + (1/30) + (1/24)] = 120/(3 + 4 + 5) = 10 days

Statements II and III together are sufficient.

So, any two of statements I, II and III together are sufficient.