As per the given all details in above question , we can say
Given , 12 men and 8 women can complete a piece of work = 10 days
Let 15 men and 4 women to complete the same work in D days .
From statement A , 15 men can complete the work = 12 days.
From statement B , 15 women can complete the work = 16 days.
From statement C , Women = ( 3 / 4 ) x men ⇒ 4W = 3M
According to question ,
( 12M + 8W ) x 10 = ( 15M + 4W ) x D
⇒ ( 4 x 4W + 8W ) x 10 = ( 5 x 4W + 4W ) x D ⇒ 24W x 10 = 24W x D ⇒ D = 10 days

Correct Option: D

As per the given all details in above question , we can say
Given , 12 men and 8 women can complete a piece of work = 10 days
Let 15 men and 4 women to complete the same work in D days .
From statement A , 15 men can complete the work = 12 days.
From statement B , 15 women can complete the work = 16 days.
From statement C , Women = ( 3 / 4 ) x men ⇒ 4W = 3M
According to question ,
( 12M + 8W ) x 10 = ( 15M + 4W ) x D
⇒ ( 4 x 4W + 8W ) x 10 = ( 5 x 4W + 4W ) x D ⇒ 24W x 10 = 24W x D ⇒ D = 10 days
Any two of the three statements are sufficient to answer the question. Hence, anyone of the statements can be dispensed with.

As per the given question , we can say From statement A , Area of the plot = πr² = 616 m² .
⇒ ( 22 / 7 ) x r² = 616 ⇒ r² = 616 x ( 7 / 22 ) = 28 x 7 = 196
⇒ r = 14 cm
From statement B , Cost of fencing a rectangular plot = $ 780 and perimeter =120 m
From statement C , Area of a square plot = a² = 196 m²
⇒ a = √196 = 14
∴ a = 14 = radius of the circular plot
From statement A , we have
Area of the plot = 616 m²
∴ Cost of fencing a circular plot = Area x Cost of fencing a rectangular plot = 616 x 780 = $ 480480

Correct Option: C

As per the given question , we can say
From statement A , Area of the plot = πr² = 616 m² .
⇒ ( 22 / 7 ) x r² = 616 ⇒ r² = 616 x ( 7 / 22 ) = 28 x 7 = 196
⇒ r = 14 cm
From statement B , Cost of fencing a rectangular plot = $ 780 and perimeter =120 m
From statement C , Area of a square plot = a² = 196 m²
⇒ a = √196 = 14
∴ a = 14 = radius of the circular plot
From statement A , we have
Area of the plot = 616 m²
∴ Cost of fencing a circular plot = Area x Cost of fencing a rectangular plot = 616 x 780 = $ 480480
(B) is necessary because only this statement gives the rate of fencing. Anyone of (A) or (C) gives the value of radius, which enables us to find the circumference.
Hence, either (A) or (C) can be dispensed with.

On the basis of above given details in question ,
Let father’s present age is F and son’s present age is S .
From statement A , Father’s present age = 2 x son’s present age
⇒ F = 2S
From statement B , After 10 years , ratio of father’s age to the son’s age = 12 : 7
⇒ ( F + 10 ) : ( S + 10 ) = 12 : 7
From statement C , 5 years ago , father’s age - son’s age = son’s present age
⇒ ( F - 5 ) - ( S - 5 ) = S
From statement B and A , we have
⇒ ( 2S + 10 ) / ( S + 10 ) = 12 / 7 { ∴ putting F = 2S }
⇒ 14S + 70 = 12S + 120 ⇒ 14S - 12S = 120 - 70 ⇒ 2S = 50 ⇒ S = 50 / 2 = 25 years and F = 2 x 25 = 50 years
After 5 years , Father’s age = Father’s present age + 5 = 50 + 5 = 55 years
and Son’s age = Son’s present age + 5 = 25 + 5 = 30 years
Sum of the ages of father and the son after five years = 55 + 30 = 85 years

Correct Option: E

On the basis of above given details in question ,
Let father’s present age is F and son’s present age is S .
From statement A , Father’s present age = 2 x son’s present age
⇒ F = 2S
From statement B , After 10 years , ratio of father’s age to the son’s age = 12 : 7
⇒ ( F + 10 ) : ( S + 10 ) = 12 : 7
From statement C , 5 years ago , father’s age - son’s age = son’s present age
⇒ ( F - 5 ) - ( S - 5 ) = S
From statement B and A , we have
⇒ ( 2S + 10 ) / ( S + 10 ) = 12 / 7 { ∴ putting F = 2S }
⇒ 14S + 70 = 12S + 120 ⇒ 14S - 12S = 120 - 70 ⇒ 2S = 50 ⇒ S = 50 / 2 = 25 years and F = 2 x 25 = 50 years
After 5 years , Father’s age = Father’s present age + 5 = 50 + 5 = 55 years
and Son’s age = Son’s present age + 5 = 25 + 5 = 30 years
Sum of the ages of father and the son after five years = 55 + 30 = 85 years
Any two of the three statements are sufficient to answer the question (As to find the two unknowns we need two equations). Hence, anyone of the statements can be dispensed with.

As per the given all details in above question , we can say that
Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
From (A) alone :

Correct Option: E

As per the given all details in above question , we can say that
Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
From (A) alone:

Then, P		1 +	r		2	= 5500 + 12.5 = 5512.5 ...(1)
			100

or, P		1 +	2r		= 5500 ...(2)
			100

As per the given all details in above question , we have'
From statement A , average of four subjects marks including English = 60 marks
Total Sum of four subjects marks = 60 x 4 = 240 marks
From statement B , Total marks in English and Mathematics together = 170 marks
From statement C , Total marks in Mathematics and Science together = 180 marks
Anyone of the three statements is not sufficient to answer the question.

Correct Option: E

As per the given all details in above question , we have
From statement A , average of four subjects marks including English = 60 marks
Total Sum of four subjects marks = 60 x 4 = 240 marks
From statement B , Total marks in English and Mathematics together = 170 marks
From statement C , Total marks in Mathematics and Science together = 180 marks
Anyone of the three statements is not sufficient to answer the question. The question cannot be answered even with the information in all the three statements.