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1. Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes
respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?

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2. A garrison of 3300 men has provisions for 32 days, when given at a rate of 850 grams per head. At the end of 7 days a reinforcement arrives and it was found that now the provisions will last 8 days less, when given at the rate of 825 grams per head. How, many more men can it feed?


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3. Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.

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4. The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?
  

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5. A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?


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6. A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?
  

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7. A certain type of mixture is prepared by mixing brand A at Rs.9 a kg. with brand B at Rs.4 a kg. If the mixture is worth Rs.7 a kg., how many kgs. of brand A are needed to make 40kgs. of the mixture?


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8. What is the missing number in this series? 8 2 14 6 11 ? 14 6 18 12


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9. Can you tender a one rupee note in such a manner that there shall be total 50 coins but none of them would be 2 paise coins.?

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10. The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten's place of the original
number is equal to twice the difference between its digits. What is the number?

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11. If Log2 x - 5 Log x + 6 = 0, then what would the value / values of x be?


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12. A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were ?
  

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13. Three cards are drawn at random from an ordinary pack of cards. Find the probability that they will consist of a king, a queen and an ace.


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14. The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?
  

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15. Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from
the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?

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ANSWERS


1. 167 min.
2. 1700 men.
3. x = 3/2 or -3 and y = 3 or -3/2..
4. 32 8/11 minutes..
5. 8.
6. 360 Years old.
7. Brand A needed is 24kgs..
8. 9.
9. 45 one paisa coins, 2 five paise coins, 2 ten paise coins, and 1 twenty-five paise coins..
10. 46.
11. x = e2 or e3.
12. 991.
13. 64/2210
14. 40 Years.
15. 46 Steps.