Data Sufficiency
Direction: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and Read both the statements and give answer
 What was the ratio between the ages of P and Q four years ago?
I. The ratio between the present ages of P and Q is 3 : 4.
II. The ratio between the present ages of Q and R is 4 : 5.

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As per the given above question ,
From statement I , The ratio present ages of P and Q = 3 : 4 .
From statement II , The ratio present ages of Q and R = 4 : 5 .
Combining the both statements , we get
Ratio of present ages of P , Q and R = 12 : 16 : 20 = 3 : 4 : 5
Let ages of P , Q and R be 3k , 4k and 5k .
4 years ago , Age of P = ( 3k  4 )
and Age of Q = ( 4k  4 )Correct Option: D
As per the given above question ,
From statement I , The ratio present ages of P and Q = 3 : 4 .
From statement II , The ratio present ages of Q and R = 4 : 5 .
Combining the both statements , we get
Ratio of present ages of P , Q and R = 12 : 16 : 20 = 3 : 4 : 5
Let ages of P , Q and R be 3k , 4k and 5k .
4 years ago , Age of P = ( 3k  4 )
and Age of Q = ( 4k  4 )
4 years ago , Ratio of P and Q = ( 3k  4 ) : ( 4k  4 )
For solving this question, we want two equations in terms of P and Q .
 What is the speed of a running train which takes 9 seconds to cross a signal post?
I. The length of the train is 90 m.
II. The train takes 27 seconds to cross a platform of 180 m.

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On the basis of above given details in question , we can say
Time taken in crosses a signal post = 9 seconds
From statement I , The length of the train = Distance = 90 m
Speed of running train = distance / time taken = 90 / 9 = 10 m / sec
From statement II , The length of platform = 180 m and time taken = 27 seconds
Speed of running train = distance / time taken = ( 90 + 180 ) / 27 = 270 / 27 = 10 m / secCorrect Option: C
On the basis of above given details in question , we can say
Time taken in crosses a signal post = 9 seconds
From statement I , The length of the train = Distance = 90 m
Speed of running train = distance / time taken = 90 / 9 = 10 m / sec
From statement II , The length of platform = 180 m and time taken = 27 seconds
Speed of running train = distance / time taken = ( 90 + 180 ) / 27 = 270 / 27 = 10 m / sec
Data either in statement I alone or in statement II alone are sufficient to answer the question.Hence , option C is correct answer .
 What selling price should be marked on the article?
I. Discount of 5% is to be given and profit percentage should be double the discount. Purchase cost is in the range of $ 300 to $ 400.
II. 10% discount is to be allowed and 15% profit is to be obtained on the purchase cost of $ 200 of the article.

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According to question ,
From statement I , → The fixed value of CP is not given, so SP of the article cannot be determined.
From statement II , → Let, K be SP of an articleCorrect Option: B
According to question ,
From statement I , → The fixed value of CP is not given, so SP of the article cannot be determined.
From statement II , → Let, K be SP of an articleK x 100  10 = 200 x ( 100 + 15 ) 100 100 K x 90 = 200 x 115 100 100 ∴ K= 200 x 115 = $ 255.55 90
Therefore , the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question .
 What is the cost of polishing the rectangular floor?
I. Room is 9 m long and 7 m wide.
II. Cost of polishing the floor of 10 m by 5 m is $ 112.50.

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On the basis of above given details in question ,
From statement I → Area of the room = L x B = 9 × 7 = 63 m^{2}From statement II → Rate = Cost of polishing the floor Area of floor Correct Option: E
On the basis of above given details in question ,
From statement I → Area of the room = L x B = 9 × 7 = 63 m^{2}From statement II → Rate = Cost of polishing the floor Area of floor Rate = 112.50 = 2.25 per m^{2} 10 x 5
∴ Combining both the statements, cost of polishing the rectangular floor = 63 × 2.25 = $ 141.75.
 How many marks did Prakash obtain in Mathematics?
I. Prakash secured on an average 55 percent marks in Mathematics, Physics and Chemistry together.
II. Prakash secured 10 percent more than the average in Mathematics.

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As per the given above question ,
From statement I , Average of mathematics , physics and chemistry = 55%
⇒ M + Ph + Ch = 165%
From statement II , Prakash → M + 10% (average)
Where , M → Mathematics , Ph → Ph and Ch → ChemistryCorrect Option: D
As per the given above question ,
From statement I , Average of mathematics , physics and chemistry = 55%
⇒ M + Ph + Ch = 165%
From statement II , Prakash → M + 10% (average)
Where , M → Mathematics , Ph → Ph and Ch → Chemistry
Hence , both statements I and II together are not sufficient to answer the question.