Ans. x = e2 or e3.
12. 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?
Ans. 46
13. 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?
Ans. 45 one paisa coins, 2 five paise coins, 2 ten paise coins, and 1 twenty-five paise coins.
14. A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. How much time would it take the monkey to reach the top?
Ans. 18 hours.
15. What is the missing number in this series? 8 2 14 6 11 ? 14 6 18 12
Ans. 9
16. 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?
Ans. 32 8/11 minutes.
17. Solve for x and y: 1/x – 1/y = 1/3, 1/x2 + 1/y2 = 5/9.
Ans. x = 3/2 or -3 and y = 3 or -3/2.
18. Daal is now being sold at Rs. 20 a kg. During last month, its rate was Rs. 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?
Ans. 20 %.
19. Find the least value of 3x + 4y if x2 y3 = 6.
Ans. 10.
20. Can you find out what day of the week was January 12, 1979?
Ans. Friday.
21. 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?
Ans. 1700 men.
22. From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball?
Ans. 3720.
23. 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?
Ans. 167 minutes.
24. A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?
Ans. 3 hours 20 minutes.
25. 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 will 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?
Ans.46 steps.