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- Question
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?
Options- A. 18 litres
- B. 24 litres
- C. 32 litres
- D. 42 litres
- Correct Answer
- 24 litres
ExplanationLet the quantity of the wine in the cask originally be x litres.Then, quantity of wine left in cask after 4 operations = [ x ❨ 1 - 8 ❩ 4 ] litres. x ∴ ❨ x(1 - (8/x))4 ❩ = 16 x 81 ⟹ ❨ 1 - 8 ❩ 4 = ❨ 2 ❩ 4 x 3 ⟹ ❨ x - 8 ❩ = 2 x 3 ⟹ 3x - 24 = 2x
⟹ x = 24.
More questions
- 1. ( x2/3)- 3/4 is equivalent to :
Options- A. 1 x
- B. 1 ?x
- C. 1 x2
- D. 1 x- 2 Discuss
Correct Answer: 1 ?x
Explanation:
- 2. The probability of getting a composite number when a six-faced unbiased die is tossed, is
Options- A. 1/4
- B. 1/3
- C. 1/2
- D. 1 Discuss
Correct Answer: 1/3
Explanation:
n(S) = 6, n(E) = (4, 6) = 2
? P(E) = 2/6 = 1/3- 3. Ajay takes some loan from Rashmi at the rate of 5% per annum andd after 2 yr, Ajay gave back ? 8800 to Rashmi and this way paid his whole loan. Find the interest by Ajay.
Options- A. ? 825
- B. ? 975
- C. ? 800
- D. ? 850 Discuss
Correct Answer: ? 800
Explanation:
Here, A = ? 8800, T =2 yr, R = 5%
We know
SI = ART/(100 + RT) = (8800 x 5 x 2) / (100 + 5 x 2)
= (8800 x 10) / 110
= ? 800- 4. 582, 605, 588, 611, 634, 617, 600
Options- A. 634
- B. 611
- C. 605
- D. 600 Discuss
Correct Answer: 634
Explanation:
Alternatively 23 is added and 17 is subtracted from the terms. So, 634 is wrong.- 5. In the given figure, AM ? BC and AN is the bisector of ?A. What is the measure of ?MAN.
Options- A. 17.5°
- B. 15.5°
- C. 20°
- D. 25° Discuss
Correct Answer: 17.5°
Explanation:
- 6. If the cost of 1/4 th of kg is Rs. 0·60, then what is the cost of 200 gm ?
Options- A. 42 paise
- B. 48 paise
- C. 40 paise
- D. 50 paise Discuss
Correct Answer: 48 paise
Explanation:
- 7. 10, 26, 74, 218, 654, 1946, 5834
Options- A. 26
- B. 74
- C. 218
- D. 654
- E. 1946 Discuss
Correct Answer: 654
Explanation:
2nd term = (1st term) x 3 - 4 = 10 x 3 - 4 = 26.3rd term = (2nd term) x 3 - 4 = 26 x 3 - 4 = 74.
4th term = (3th term) x 3 - 4 = 74 x 3 - 4 = 218.
5th term = (4th term) x 3 - 4 = 218 x 3 - 4 = 650.
∴ 5th term must be 650 instead of 654.
- 8. One side of a rectangular field is 4 meter and its diagonal is 5 meter. The area of the field is?
Options- A. 12 m2
- B. 15 m2
- C. 20 m 2
- D. 4?5 m2 Discuss
Correct Answer: 12 m2
Explanation:
Other side = ?5 2 - 42
= ? 9
=3 m
So The area of the rectangular field = 4 x 3
= 12 m2- 9. Convert 0.2 7 into a vulgar fraction.
Options- A. 5/18
- B. 5/19
- C. 7/19
- D. 3/17 Discuss
Correct Answer: 5/18
Explanation:
0.27 = (27 - 2)/90 = 25/90 = 5/18
- 10. If in a hostel 45 days, food is available food is available for 50 students, for how many days will this food be sufficient for 75 students?
Options- A. 25 days
- B. 28 days
- C. 30 days
- D. 40 days Discuss
Correct Answer: 30 days
Explanation:
For 50 students, food is sufficient for 45 days
? For 1 student, food is sufficient for 45 x 50 days
and for 75 students, food is sufficient for (45 x 50)/75 days. i,e., for 30 days.
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