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- Question
An amount of 5,000 is invested at a fixed rate of 8 per cent per annum. What amount will be the value of the investment in five years time, if the interest is compounded every six months?
Options- A. 7401.22
- B. 3456
- C. 4567
- D. 7890
- Correct Answer
- 7401.22
ExplanationWith slight modifications, the basic formula can be made to deal with compounding at intervals other than annually.
Since the compounding is done at six-monthly intervals, 4 per cent (half of 8 per cent) will be added to the value on each occasion.
Hence we use r = 0.04. Further, there will be ten additions of interest during the five years, and so n = 10. The formula now gives:
V = P(1 + r)10 = 5,000 x (1.04)10 = 7,401.22
Thus the value in this instance will be £7,401.22.
In a case such as this, the 8 per cent is called a nominal annual
rate, and we are actually referring to 4 per cent per six months.
- 1. The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?
Options- A. 25% increase
- B. 50% increase
- C. 50% decrease
- D. 75% decrease Discuss
- 2. If log10 2 = 0.3010, the value of log10 80 is:
Options- A. 1.6020
- B. 1.9030
- C. 3.9030
- D. None of these Discuss
- 3. A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
Options- A. 2 p.m. on Tuesday
- B. 2 p.m. on Wednesday
- C. 3 p.m. on Thursday
- D. 1 p.m. on Friday Discuss
- 4. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Options- A. 15360
- B. 153600
- C. 30720
- D. 307200 Discuss
- 5. The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Options- A. 9 cm
- B. 18 cm
- C. 20 cm
- D. 41 cm Discuss
- 6. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
Options- A. 2 : 5
- B. 3 : 7
- C. 5 : 3
- D. 7 : 3 Discuss
- 7. How many times in a day, are the hands of a clock in straight line but opposite in direction?
Options- A. 20
- B. 22
- C. 24
- D. 48 Discuss
- 8. The last day of a century cannot be
Options- A. Monday
- B. Wednesday
- C. Tuesday
- D. Friday Discuss
- 9. In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:
Options- A. 40 sec
- B. 47 sec
- C. 33 sec
- D. None of these Discuss
- 10. How many times are the hands of a clock at right angle in a day?
Options- A. 22
- B. 24
- C. 44
- D. 48 Discuss
More questions
Correct Answer: 50% increase
Explanation:
Original area = xy.
| New length = | x | . |
| 2 |
New breadth = 3y.
| New area = | ❨ | x | x 3y | ❩ | = | 3 | xy. |
| 2 | 2 |
| ∴ Increase % = | ❨ | 1 | xy x | 1 | x 100 | ❩% | = 50%. |
| 2 | xy |
Correct Answer: 1.9030
Explanation:
| log10 80 | = log10 (8 x 10) |
| = log10 8 + log10 10 | |
| = log10 (23 ) + 1 | |
| = 3 log10 2 + 1 | |
| = (3 x 0.3010) + 1 | |
| = 1.9030. |
Correct Answer: 2 p.m. on Wednesday
Explanation:
| ∴ The watch gains | ❨ | 2 + 4 | 4 | ❩min. | or | 34 | min. in 170 hrs. |
| 5 | 5 |
| Now, | 34 | min. are gained in 170 hrs. |
| 5 |
| ∴ 2 min. are gained in | ❨ | 170 x | 5 | x 2 | ❩hrs | = 50 hrs. |
| 34 |
∴ Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.
Correct Answer: 153600
Explanation:
| Perimeter = Distance covered in 8 min. = | ❨ | 12000 | x 8 | ❩m = 1600 m. |
| 60 |
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
∴ Length = 480 m and Breadth = 320 m.
∴ Area = (480 x 320) m2 = 153600 m2.
Correct Answer: 18 cm
Explanation:
Also, lb = 20.
(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81
⟹ (l + b) = 9.
∴ Perimeter = 2(l + b) = 18 cm.
Correct Answer: 5 : 3
Explanation:
| Let 40% of A = | 2 | B |
| 3 |
| Then, | 40A | = | 2B |
| 100 | 3 |
| ⟹ | 2A | = | 2B |
| 5 | 3 |
| ⟹ | A | = | ❨ | 2 | x | 5 | ❩ | = | 5 |
| B | 3 | 2 | 3 |
∴ A : B = 5 : 3.
Correct Answer: 22
Explanation:
So, in a day, the hands point in the opposite directions 22 times.
Correct Answer: Tuesday
Explanation:
100 years contain 5 odd days.
∴ Last day of 1st century is Friday.
200 years contain (5 x 2) ≡ 3 odd days.
∴ Last day of 2nd century is Wednesday.
300 years contain (5 x 3) = 15 ≡ 1 odd day.
∴ Last day of 3rd century is Monday.
400 years contain 0 odd day.
∴ Last day of 4th century is Sunday.
This cycle is repeated.
∴ Last day of a century cannot be Tuesday or Thursday or Saturday.
Correct Answer: 33 sec
Explanation:
| ∴ B covers 200 m in | ❨ | 7 | x 200 | ❩ | = 40 sec. |
| 35 |
B's time over the course = 40 sec.
∴ A's time over the course (40 - 7) sec = 33 sec.
Correct Answer: 44
Explanation:
∴ In 24 hours, they are at right angles 44 times.
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