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- Question
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Options- A. 173 m
- B. 200 m
- C. 273 m
- D. 300 m
- Correct Answer
- 273 m
Explanation
Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, ∠ACB = 30° and ∠ADB = 45°.
AB = tan 30° = 1 ⟹ AC = AB x √3 = 100√3 m. AC √3 AB = tan 45° = 1 ⟹ AD = AB = 100 m. AD ∴ CD = (AC + AD) = (100√3 + 100) m = 100(√3 + 1) = (100 x 2.73) m = 273 m. - 1. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Options- A.
1 2 - B.
2 5 - C.
8 15 - D.
9 20
Discuss
- 2. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
Options- A.
1 13 - B.
3 13 - C.
1 4 - D.
9 52
Discuss
- 3. Efficiency of Asha is 25% more then Usha and Usha takes 25 days to complete a piece of work. Asha started a work alone and then usha joined her 5 days before actual completion of the work. For how many days Asha worked alone?
Options- A. 9
- B. 11
- C. 10
- D. 15 Discuss
- 4. kavita, babita and samita started a work. 5 days later Samita left the work and Babita left the work after working 8 days. In how many more days Kavita would have completed the rest work if they take 20, 60 and 30 days individually to finish a work?
Options- A. 4
- B. 5
- C. 6
- D. 8 Discuss
- 5. In a school, MID-Day meal food is sufficient for 250 students for 33 days. if each students is given 125 g meals. 80 more students joined the school. If same amount of meal is given to each student, then the food will last for
Options- A. 20 days
- B. 40 days
- C. 30 days
- D. 25 days Discuss
- 6. The average salary of A, B is Rs. 6000 and that of C, D and E is Rs. 8000. The average salary of all the 5 people is
Options- A. Rs.7200
- B. Rs. 7000
- C. Rs. 7500
- D. can't be determined Discuss
- 7. Mr. Modi can copy 40 pages in 10 minutes, Mr. Xerox and Mr. Modi both working together can copy 250 In 25 minutes. In how many minutes Mr. Xerox can copy 36 pages?
Options- A. 5 minutes
- B. 6 minutes
- C. 3 minutes
- D. 12 minutes Discuss
- 8. A can run a distance of 1 Km in 3 minutes 10 seconds and B can run the same distance in 3 minutes 20 seconds. If they start together, by what distance will A beat B?
Options- A. 50 m
- B. 30 m
- C. 36 m
- D. 60 m Discuss
- 9. There are 10 points in a plan, out of which 5 are collinear. Find the number of straight lines formed by joining them.
Options- A. 36
- B. 45
- C. 30
- D. 35 Discuss
- 10. A can do a piece of work in 10 days, while B can do it in 6 days. B worked at it for 4 days. How long will A take to finish the remaining work?
Options- A. 31/3 days
- B. 32/3 days
- C. 32/5 days
- D. 35/7 Discuss
More questions
Correct Answer:
| 9 |
| 20 |
Explanation:
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
| ∴ P(E) = | n(E) | = | 9 | . |
| n(S) | 20 |
Correct Answer:
| 3 |
| 13 |
Explanation:
| ∴ P (getting a face card) = | 12 | = | 3 | . |
| 52 | 13 |
Correct Answer: 11
Explanation:
Efficiency (Asha : Usha) = 5 : 4
Number of days(Asha : Usha) = 4x : 5x = 4x : 25
? Number of days required by Asha to finish the work alone = 4x
= 4 x 5 = 20.
Now, since Asha and Usha did work together for last 5 days = 5 x 9 = 45%
(since efficiency of Asha = 5% and Usha's efficiency = 4%)
It means Asha completed 55% work alone.
? No. of days taken by Asha to complete 55% work = 55/5 = 11days
Correct Answer: 6
Explanation:
Efficiency of Kavita = 5%
Efficiency of Babita = 1.66%
Efficiency of Samita = 3.33%
Work done in 5 days by K + B + S = 5 x 10 = 50%
Work done in 3 days by K + B = 3 x 6.66 = 20%
Remaning work (30%) done by Kavita alone = 30/5 = 6 days
Correct Answer: 25 days
Explanation:
M1 = 250, D 1 = 33 days
per day meal W1 = W2 = 125 g
M2 = (250 + 80) =330 and D2=?
According to the formula
M1D1W2 = M2D2W1
250 x 33 x 125 = 330 x D2x 125
? D2 = (250 x 33)/330
? D2 = 25 days
Correct Answer: Rs.7200
Explanation:
Required average salary
= ( 6000 x 2 + 8000 x 3) / (2 + 3 )
= 36000 / 5
= Rs. 7200
Correct Answer: 6 minutes
Explanation:
Efficiency ( per minute) of Modi = 4 copies/min
Efficiency of Modi and Xerox together = 10 pages/min
? Efficiency of Xerox alone = 10 - 4 = 6 pages/min
? Mr. Xerox needs 6 min to copy 36 pages.
Correct Answer: 50 m
Explanation:
According to question,
A can run a distance of 1 Km in 3 minutes 10 seconds and B can run the same distance in 3 minutes 20 seconds.
A beats B by 10 sec.
So distance covered by B in 10 sec. = (1000 *10 / 200) m = 50 m
? A beat B by 50 m.
Correct Answer: 36
Explanation:
Required number of straight lines
=nC2 - mC2 + 1
Here, n = 10, m = 5
= 10C2 - 5C2 + 1
= 45 - 10 + 1 = 36
Correct Answer: 31/3 days
Explanation:
B's 4 days work = (1/6) x 4 = 2/3
? Remaining work = 1 - (2/3) = 1/3
A's 1 day's work = 1/10
? 1/3 work is finished by A in
(10 x 1/3) = 31/3 days
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