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Q1. Two pipes A and B can fill a tank in 15 hours and 20 hours respectively while a third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed, In how much time, will the tank be full?
Q2. Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the cistern, it takes 32 minutes extra for the cistern to be filled up. When the cistern is full, in what time will the leak empty it ?
Q3. The ratio between the speed of a train and a car is 6 : 1 respectively. Also, a bus covered a distance of 480 kms in 12 hours. The speed of the bus is five–ninths the speed of the train. How much distance will the car cover in 5 hours?
Q4. Train-A crosses a pole in 25 seconds and another Train-B crosses as pole in 1 minute and 15 seconds. The Length of the train-A is half the length of the train-B. What is the respective ratio between the speed of the train-A and the train-B ?
Q5. A, B and C can do a work in 8, 16 and 24 days respectively. They all begin together. A continues to work till it is finished, C leaving off 2 days and B one day before its completion. In what time is the work finished?
Directions (6-10): In each of these questions, two equations numbered I and II are given. You have to solve both the equation and give answer
Q6. I. x² + x - 12 = 0
II. y² - 5y + 6 = 0
Q7. I. x² + 9x + 18 = 0
II. y² - 13y + 40 = 0
Q8. I. x² – 6x = 7
II. 2y² + 13y + 15 = 0
⇒ x² – 7x +x– 7 = 0
⇒ x (x – 7) +1(x – 7) = 0
⇒ (x + 1) (x – 7) = 0
⇒ x = –1 or 7
II. 2y² + 13y + 15 = 0
⇒ 2y² + 3y + 10y + 15 = 0
⇒ y (2y + 3) + 5 (2y + 3) = 0
⇒ (y + 5) (2y + 3) = 0
⇒ y = –5 or -3/2
∴ x > y
Q9. I. x² – (1+√2) x + √2 = 0
II. y² – 3y + 2 = 0
⇒ x (x - 1) – √2 (x - 1) = 0
⇒ (x - √2)(x - 1) = 0
⇒ x = √2 or 1
II. y² – 3y +2 = 0
⇒ y² - 2y – y+ 2 = 0
⇒ y (y – 2) – 1 (y - 2) = 0
⇒ (y - 1) (y - 2) = 0
⇒ y = 1 or 2
∴ Relation cannot be established between x and y.
Q10. I. x² – 463 = 321
II. y² – 421 = 308
∴ x = ±28
II.y² = 308 + 421 = 729
∴ y = ±27
Relation cannot be established between x and y.
Directions (11-15): Study the following graph carefully and answer the questions given below:
Q11. What was the average profit earned by all the three companies in the year 2008 ?
Q12. In which of the following years was the difference between the profits earned by company B and company A the minimum ?
Q13. In which of the following years was the total profit earned by all three companies together the highest ?
= 400 + 425 + 475
Q14. What was the approximate percentage increase in the profit earned by Company A from 2006 to 2007 ?
Q15. What was the difference between the profit earned by company A in 2004 and the profit earned by company C in 2009 ?
= 400 – 300
= 100 crore
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