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In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects. Find the number of students who had taken both Physics and Chemistry but not Mathematics.
In a survey of university students, 64 had taken Drama course, 94 had taken Dance course, 58 had taken a Singing course, 28 had taken Drama and singing course, 26 had taken Drama and dance course, 22 had taken Dance and singing course, and 14 had taken all the three courses. Find how many have taken only one course?
Consider the following statements concerning railways: 1. A level stretch equal to the maximum train length is to be provided between the gradient reaches where a rising gradient is followed by a falling gradient. 2. Vertical curves in railway tracks are not set out as parabolas. 3. Diamond crossings can be laid on curves also. 4. Curves should be avoided at the top level segment of bridges. Which of the above statements are correct?
A Time taken by pipe P and Q to fill the tank is 120/23 minutes. Time taken by drain pipe S to empty the tank is 12 minutes more than pipe P to fill the tank. Time taken by pipe Q is 15 minutes. Ratio of time taken by R to fill up the tank and by pipe Q is 4 : 5. What is total time taken to fill the whole tank when all the pipes are open? 
Time taken by pipe A and pipe B to fill up the cistern is 12 minutes whereas time taken by pipe C to empty the whole cistern is twice that of time taken by A and B together to fill the tank and ratio of time taken by pipe A and B to fill up the tank when operating alone is 2 : 3. If pipe A and B are alternatively opened every 6 minutes and C is opened with pipe B but closed when pipe A is opened then calculate total time taken to fill up the whole cistern. 
A can finish a work in half the time taken by B to finish the work. The time taken by C to finish the work is equal to the total time taken by A and B together to finish the work. What is the ratio of the time taken to finish the work when A, B and C work together to that of the time taken by A working alone?
Time taken by pipe P and Q to fill up the tank is 60/ 7 minutes and time taken to fill the whole tank when all three pipes are open is 300/ 23 minutes. Ratio of time taken by pipe P to fill up the tank and pipe Q is 3 : 4. Calculate time taken by Q and R to fill up the tank. (Pipe R is a drain pipe.)
In a group of 450 students, 22% of the total students take the Hindi subject, 34% of the total students take the Physics subject, and 26% of the total students take the Social Science subject. 8% of the total students have taken both Hindi and Physics subject only. Out of the total students in the Hindi subject, 1/3 have taken both Hindi and Social Science subject only. Out of the total students in the Physics subject, 1/3 have taken both Physics and Social Science subject only. Only 20 students take all the three subjects. Find the number of students who have not taken any subject.  
In a group of 450 Teachers, 22% of the total Teachers take the English department, 34% of the total Teachers take the quant. department, and 26% of the total Teachers take the LR department. 8% of the total Teachers have taken both English and quant department only. Out of the total Teachers in the English department, 1 / 3 have taken both English and LR department only. Out of the total Teachers in the quant department, 1 / 3 have taken both quant and LR department only. Only 20 Teachers take all the three departments. Find the number of Teachers who have not taken any department. 
Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. Two person X and Y together can make 25% of total number of bricks in 4.8 days. Another person Z can make 50 bricks in a day. What is the time taken by person X and Z together to make the total number of bricks? I. Dimensions of a brick is (3cm × 4cm × 5cm) while the dimension of a cuboids when all the bricks are put together is (72cm × 80cm × 50cm) and ratio of number of days taken by X and Y alone to make the total number of bricks is 3 : 2. II. The total number of bricks is 4800 and person Y can make 150 bricks in day. III. Total volume of all the bricks together is 1.008m3 and dimension of a bricks is (5cm × 6cm × 7cm) and time taken by Z to make total number of bricks is 200 % more than the total time taken by person Y to make total number of bricks.