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- Question
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
Options- A. 6 hours
- B. 10 hours
- C. 15 hours
- D. 30 hours
- Correct Answer
- 15 hours
ExplanationSuppose, first pipe alone takes x hours to fill the tank .Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
∴ 1 + 1 = 1 x (x - 5) (x - 9) ⟹ x - 5 + x = 1 x(x - 5) (x - 9) ⟹ (2x - 5)(x - 9) = x(x - 5)
⟹ x2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
⟹ x = 15. [neglecting x = 3]
More questions
- 1. A train 300 meters long passes a standing man is 15 seconds. The speed of the train is?
Options- A. 40 km/hr
- B. 50 km/hr
- C. 60 km/hr
- D. 72 km/hr Discuss
Correct Answer: 72 km/hr
Explanation:
? Speed = Distance / Time = (300/15)
= 20 m/sec
= (20 x 18) / 5 = 72 km/hr- 2. If the diagonal of a square is double, how does the area of the square change?
Options- A. Becomes four fold
- B. Becomes three fold
- C. Becomes two fold
- D. None of the above Discuss
Correct Answer: Becomes four fold
Explanation:
Ratio of the areas = area of original square / area of new square
= [ d2 / 2 ] / [ (2d)2 / 2 ] = 1/4
? New area becomes 4 fold.- 3. 46080, 3840, 384, 48, 24, 2, 1
Options- A. 1
- B. 2
- C. 24
- D. 384 Discuss
Correct Answer: 24
Explanation:
The terms are successively divided by 12, 10, 8, 6, ...etc.So, 24 is wrong, it should be 8 (48/6 = 8).
- 4. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Options- A. 1520 m2
- B. 2420 m2
- C. 2480 m2
- D. 2520 m2 Discuss
Correct Answer: 2520 m2
Explanation:
We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.Solving the two equations, we get: l = 63 and b = 40.
∴ Area = (l x b) = (63 x 40) m2 = 2520 m2.
- 5. 4/5 of a number exceeds its 2/3 by 8. The number is?
Options- A. 30
- B. 60
- C. 90
- D. None of these Discuss
Correct Answer: 60
Explanation:
Let the number be x,
Then, 4x/5 - 2x/3 = 8
? (12x - 10x) / 15 = 8
? 2x = 120
? x = 60- 6. Find the angle between minute hand and hour hand at 2 : 18 AM
Options- A. 37°
- B. 33°
- C. 39°
- D. None of these Discuss
Correct Answer: 39°
Explanation:
39°
- 7. Rakesh, Dinesh and Mahesh start a business by investing ? 5000 , ? 8000 and ? 12000 , respectively . At the end of year, they got the profit of ? 12500. What is the share of Dinesh in profit?
Options- A. ? 4000
- B. ? 4500
- C. ? 6000
- D. ? 7500 Discuss
Correct Answer: ? 4000
Explanation:
Share of Rakesh : Share of Dinesh : Share of Mahesh
= 5000 : 8000 : 12000 = 5 : 8 : 12
Total earned profit = ? 12500
? Share of Dinesh in profit
= [8/(5 + 8 + 12)] x 12500 = (8/25) x 12500
= 8 x 500 = ? 4000- 8. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
Options- A. 74
- B. 94
- C. 184
- D. 364 Discuss
Correct Answer: 364
Explanation:
L.C.M. of 6, 9, 15 and 18 is 90.Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
∴ Required number = (90 x 4) + 4 = 364.
- 9. If log 27 = 1.431, then the value of log 9 is:
Options- A. 0.934
- B. 0.945
- C. 0.954
- D. 0.958 Discuss
Correct Answer: 0.954
Explanation:
log 27 = 1.431⟹ log (33 ) = 1.431
⟹ 3 log 3 = 1.431
⟹ log 3 = 0.477
∴ log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
- 10. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
Options- A. 32
- B. 48
- C. 64
- D. 96
- E. None of these Discuss
Correct Answer: 64
Explanation:
We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).∴ Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3) = ❨ 3 x 6 x 5 ❩ + ❨ 3 x 2 x 6 ❩ + 1 2 x 1 2 x 1 = (45 + 18 + 1) = 64.
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