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- Question
- An observer measures angles of elevation of two tower of equal height from a point between the towers. If the angles of elevation are 60° and 30° and distance of nearer tower is 100 m then the height of each tower and the distance between the towers, respectively are
Options- A. 100/?3 m and 300 m
- B. 100/?3 m and 400 m
- C. 100?3 m and 300 m
- D. 100?3 m and 400 m
- Correct Answer
- 100/?3 m and 400 m
ExplanationLet us draw a figure below as per given question.
Let AB = CD = h meter be the heights of the towers. E is a point such that DE = 100 meter;
?CED = 60° and ?AEB = 30°
Now, BE = x meter (say)
From right triangle CDE.
h = 100 tan 60°
? h = 100?3 meter
From right triangle ABE,
x = h cot 30° put the value of h, we will get
x = 100?3 X ?3
x = 100 X 3 = 300 meters
Distance between the tower = DE + EB = 100 + 300 = 400 meters
Height of the tower = h = 100?3 meter - 1. A, B and C are employed to do a piece of work for $575. A and C are supposed to finish 19 / 23 of the work together. Amount shall be paid to B is:
Options- A. $210
- B. $100
- C. $200
- D. $475 Discuss
- 2. Which one of the following can't be the square of natural number?
Options- A. 32761
- B. 81225
- C. 42437
- D. 20164
- E. None of these Discuss
- 3. A number gets reduced to its one-third, when 48 is subtracted from it. What is two-third of that number?
Options- A. 24
- B. 72
- C. 36
- D. None of these Discuss
- 4. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:
Options- A. 14 2⁄7% gain
- B. 15% gain
- C. 14 2⁄7% loss
- D. 15 % loss Discuss
- 5. E being always in the middle.
Options- A. 18 ways
- B. 24 ways
- C. 48 ways
- D. 20 ways Discuss
- 6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options- A. 65 sec
- B. 89 sec
- C. 100 sec
- D. 150 sec Discuss
- 7. X can completed a job in 12 days. If X and Y work together, they can complete the job in 6 2/ 3 days, Y alone can complete the job in
Options- A. 10 days
- B. 12 days
- C. 15 days
- D. 18 days Discuss
- 8. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options- A. 3.6
- B. 6
- C. 18
- D. Cannot be determined
- E. None of these Discuss
- 9. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Options- A. 23 m
- B. 23 2⁄9 m
- C. 27 7⁄9 m
- D. 29 m Discuss
- 10. Find the number of ways, in which 12 different beads can be arranged to form a necklace .
Options- A. 11 !/2
- B. 10 !/2
- C. 12 !/2
- D. Couldn't be determined Discuss
More questions
Correct Answer: $100
Explanation:
Correct Answer: 42437
Explanation:
The square of a natural number never ends in 7.
∴42437 is not the square of a natural number.
Correct Answer: None of these
Explanation:
Let the number be N.
Then, N - N/3 = 48
2N/3 = 48.
Correct Answer: 14 2⁄7% gain
Explanation:
| C.P. of 1 orange = Rs. | ❨ | 350 | ❩ | = Rs. 3.50 |
| 100 |
| S.P. of 1 orange = Rs. | ❨ | 48 | ❩ | = Rs. 4 |
| 12 |
| ∴ Gain% = | ❨ | 0.50 | x 100 | ❩% | = | 100 | % = 14 | 2 | % |
| 3.50 | 7 | 7 |
Correct Answer: 24 ways
Explanation:
When E is fixed in the middle, then there are four places left to be filled by four remaining letters O, M, G and A and this can be done in 4! ways.
? Total number of ways = 4! = 24
Correct Answer: 89 sec
Explanation:
| Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
| 24 |
| ∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
| 10 |
Correct Answer: 15 days
Explanation:
X's 1 day's work = 1/12
(X + Y)' s 1 day's work = 3/20
? Y's 1 day's work = (3/20) - (1/12) = 4/60 = 1/15
? Number of day's taken by Y to complete the work = 15 days
Correct Answer: 6
Explanation:
Let rate = R% and time = R years.
| Then, | ❨ | 1200 x R x R | ❩ | = 432 |
| 100 |
⟹ 12R2 = 432
⟹ R2 = 36
⟹ R = 6.
Correct Answer: 27 7⁄9 m
Explanation:
| Relative speed = (40 - 20) km/hr = | ❨ | 20 x | 5 | ❩ | m/sec = | ❨ | 50 | ❩ | m/sec. |
| 18 | 9 |
| ∴ Length of faster train = | ❨ | 50 | x 5 | ❩ | m = | 250 | m = 27 | 7 | m. |
| 9 | 9 | 9 |
Correct Answer: 11 !/2
Explanation:
Number of arrangements of beads = (12 - 1) !, but it is not mentioned that either it is clockwise or anti - clockwise .
So, required number of arrangements = [(12 - 1)! ] / 2 = 11 !/2
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