As per the given all details in above question ,
From statement A , Time taken by train‘X’ = 6 seconds
From statement B , Ratio of the speeds of trains ‘X’ and ‘Y’ = 3 : 2
Let speed of train X is 3k and speed of train Y is 2k.
Relative speed = 3k + 2k = 5k
From statement C , Length of the two trains = 500 m
Time taken = Length of the two trains / Relative speed = 500 / 5k = 100 / k seconds
Anyone of the three statements is not sufficient to answer the question. So, anyone is not suitable statements.

Correct Option: E

As per the given all details in above question ,
From statement A , Time taken by train‘X’ = 6 seconds
From statement B , Ratio of the speeds of trains ‘X’ and ‘Y’ = 3 : 2
Let speed of train X is 3k and speed of train Y is 2k.
Relative speed = 3k + 2k = 5k
From statement C , Length of the two trains = 500 m
Time taken = Length of the two trains / Relative speed = 500 / 5k = 100 / k seconds
Anyone of the three statements is not sufficient to answer the question. So, anyone is not suitable statements.The question cannot be answered even with the information in all the three statements.

On the basis of above given details in question , we have
The ratio of investing money for 3 years = 5 : 4 : 2
Let the investment of X , Y and Z are 5k , 4k and 2k respectively .
From statement A , Total amount invested in the business = $ 22000.
From statement B , Profit was distributed after a period of 2 years.
From statement C , The average amount of profit earned = $ 2750.
According to question ,
Sum of investment money = Total profit
⇒ 5k + 4k + 2k = 2750 ⇒ 11k = 2750 ⇒ k = 2750 / 11 = $ 250
Amount received by X = 10k = 10 x 250 = $ 2500 ( for 2 years )

Correct Option: D

On the basis of above given details in question , we have
The ratio of investing money for 3 years = 5 : 4 : 2
Let the investment of X , Y and Z are 5k , 4k and 2k respectively .
From statement A , Total amount invested in the business = $ 22000.
From statement B , Profit was distributed after a period of 2 years.
From statement C , The average amount of profit earned = $ 2750.
According to question ,
Sum of investment money = Total profit
⇒ 5k + 4k + 2k = 2750 ⇒ 11k = 2750 ⇒ k = 2750 / 11 = $ 250
Amount received by X = 10k = 10 x 250 = $ 2500 ( for 2 years )
When investment ratio is given, the amount of profit can be found out with the help of C only.

Let, the length and breadth of the rectangle be l and b, respectively.
From statement A → Diagonal of rectangle ( h ) = 5 ⇒ l² + b² = 25
From statement B → l + b + h = 4b ⇒ l = 3b − 5

Correct Option: B

Let, the length and breadth of the rectangle be l and b, respectively.
From statement A → Diagonal of rectangle ( h ) = 5 ⇒ l² + b² = 25
From statement B → l + b + h = 4b ⇒ l = 3b − 5
From statement C → One of the angles of the triangle = 60°
From statement A and B , ( 3b - 5 )² + b² = 25 ⇒ 9b² + 25 - 30b + b² = 25
⇒ 9b² - 30b + b² = 0 ⇒ 10b² - 30b = 0 ⇒ 10b( b - 3 ) = 0 ⇒ b = 3 cm
∴ l = 3 x 3 - 5 = 9 - 5 = 4 cm
∴ Area of right angle triangle = ( 1 / 2 ) x base x height
= ( 1 / 2 ) x 3 x 4 = 6 cm²
After combining any of the above two statements, we get the values of l and b. Hence, any of them 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.

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.
Hence , A or B or C is required answer .

As per the given above question ,
Statement (B) is useless because it is the same as the given statement. [Profit is distributed in the same ratio as their investment. Since their investments are in ratio 5 : 3 : 2, the profit of P (= 5) is equal to the profit of Q and R together (3 + 2 = 5)]
Statement (A) alone is sufficient to answer.

Correct Option: A

As per the given above question ,
Statement (B) is useless because it is the same as the given statement. [Profit is distributed in the same ratio as their investment. Since their investments are in ratio 5 : 3 : 2, the profit of P (= 5) is equal to the profit of Q and R together (3 + 2 = 5)]
Statement (A) alone is sufficient to answer.
(Q's share = $ 2400