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- Question
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
Options- A. 3 : 7
- B. 7 : 3
- C. 6 : 7
- D. 7 : 6
- Correct Answer
- 7 : 3
ExplanationΠr2h = 924 ⟹ r = ❨ 924 x 2 ❩ = 7 m. 2Πrh 264 264 And, 2Πrh = 264 ⟹ h = ❨ 264 x 7 x 1 x 1 ❩ = 6m. 22 2 7 ∴ Required ratio = 2r = 14 = 7 : 3. h 6 - 1. At a game of billiards A can give B 6 points in 50 and he can give C 13 points in 65, how many points can B give C in a game of 55?
Options- A. 7
- B. 8
- C. 5
- D. 10 Discuss
- 2. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options- A. 76 kg
- B. 76.5 kg
- C. 85 kg
- D. Data inadequate
- E. None of these Discuss
- 3. Three men Ram, Karan and Mohan run around an oval garden from a fixed post at the rates of 5, 5 1? 7, 5 1? 3 per hour. They come back to the fixed post in 3 3? 4 hours. Find the greatest length, the race course can have.
Options- A. 28 / 5 km
- B. 5 / 28 km
- C. 11 / 28 km
- D. 28 / 11 km Discuss
- 4. Value of ?5 + 2?6 - 1/?5 - 2?6 is
Options- A. 2?2
- B. 0
- C. 2?3
- D. ?5 - 1 Discuss
- 5. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
Options- A. 70 km/hr
- B. 75 km/hr
- C. 84 km/hr
- D. 87.5 km/hr Discuss
- 6. The present ages of Vikas and Vishal are in the ratio 15:8. After ten years , their ages will be in the ratio 5:3. Find their present ages
Options- A. 60 years, 32 years
- B. 32 years,60 years
- C. 15 years,8 years
- D. 8 years,15 years Discuss
- 7. A person on tour has total ?360 for his daily expenses. He decides to extend his tour programme by 4 days which leads to cutting down daily expenses by ?3 a day . The numbers of days of tour are :
Options- A. 15
- B. 20
- C. 18
- D. 16 Discuss
- 8. 7 6n - 6 6n, where n is an integer greater than 0, is divisible by
Options- A. 13
- B. 127
- C. 559
- D. None of these Discuss
- 9. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet next at the starting point again?
Options- A. 46 minutes 12 seconds
- B. 45 minutes
- C. 42 minutes 36 seconds
- D. 26 minutes 18 seconds Discuss
- 10. If n is any odd number greater than 1, then n( n 2 -1 ) is
Options- A. divisible by 96 always
- B. divisible by 48 always
- C. divisible by 24 always
- D. None of these Discuss
More questions
Correct Answer: 5
Explanation:
In a game of 50, If A scores 50 then B scores 44.
? A scores 65 while B 44 * 65 / 50 = 57.2 points
Now, B scores 57.2 points while C 52
? B scores 55 points while C = 52 * 55 / 57.2 = 50
Hence, in game of 55 points B can give C (55 ? 50) = 5 points
Correct Answer: 85 kg
Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Correct Answer: 5 / 28 km
Explanation:
Total number of rounds made by Ram in 15 / 4 hrs = 5 × 15 / 4 = 75 / 4
? Total number of rounds made by Karan in 15 / 4 hrs = 36 / 7 * 15 / 4 = 135 / 7
Total number of rounds made by Mohan in 15 / 4 hrs = 16 / 3 * 15 / 4 = 20
H.C.F. of 75 / 4 , 135 / 7 and 2 = 5 / 28
Correct Answer: 0
Explanation:
?5 + 2?6 - 1/?5 - 2?6
= ((?5 + 2?6 x ?5 - 2?6 ) - 1)/?5 - 2?6
Apply the formula of Algebra.
( a + b ) x (a - b ) = a2 - b2
= (?(5)2 - (2?6 )2 - 1)/?5 - 2?6
= (?25 - 4 x 6 - 1) /?5 - 2?6
= (?25 - 24 - 1) /?5 - 2?6
= (? 1 - 1 )/?5 - 2?6
= (1 - 1 )/?5 - 2?6
= 0/?5 - 2?6
= 0
Correct Answer: 87.5 km/hr
Explanation:
| Then, 8x = | ❨ | 400 | ❩ | = 100 |
| 4 |
| ⟹ x = | ❨ | 100 | ❩ | = 12.5 |
| 8 |
∴ Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Correct Answer: 60 years, 32 years
Explanation:
Method 1
Let us assume the ratio factor is x.
Therefor the present ages of Vikas and Vishal be 15x years and 8x years.
After 10 years
vikas's age = 15x + 10 and Vishal' age = 8x + 10
According to question,
(15x+10)/(8x+10) = 5/3
? 3(15x + 10) = 5(8x + 10)
? 45x + 30 = 40x + 50
? 5x =20
? x = 20/5
? x = 4
Therefore Present age of Vikas = 15x = 15 x 4 = 60 years
and Present age of Vishal = 8x = 8 x 4 = 32 years
Method 2
Let us assume the present age of Vikas = x years and Vishal's present year = y years
According to question,
Present age of Vikas/ Present age of Vishal = 15/8
? x/y = 15/8
? 8x = 15y
? 8x - 15y = 0
? x = 15y/8 .................................(1)
After 10 years Vikash age = x + 10 and vishal age = y + 10
Ratio of age after 10 years = 5/3
(x + 10)/(y + 10) = 5/3
? 3(x + 10) = 5(y + 10)
? 3x + 30 = 5y + 50
? 3x - 5y = 50 - 30
? 3x - 5y = 20 ................................(2)
Put the value of x from equation (1) in above equation (2).
? 45y/8 - 5y = 20
? 45y - 40y = 20 x 8
? 5y = 20 x 8
? y = 4 x 8 = 32
Put the value of Y in equation (1)
x = 15 x 32/8 = 15 x 4 = 60
Therefore Present age of Vikas = x = 60 years
and Present age of Vishal = y = 32 years
Correct Answer: 20
Explanation:
Method 1 to solve this question.
Let us assume the numbers of days of tour before extending the tour are D and daily expenses is E.
According to question,
Total expenses on tour = per day expenses x total number of days
Total expenses on tour = E x D = ED
360 = ED
? ED = 360
? E = 360/D .................(1)
Again according to question,
After extending the tour by 4 days, Number of days of tour = D + 4
Expenses will be reduced by 3 rupees, then everyday expenses = E - 3
so total expenses = (D + 4) x (E - 3)
360 = (D + 4) x (E - 3)
(D + 4) x (E - 3) = 360 .............................................(2)
Put the value of E in Equation (2). we will get,
(D + 4) x (360/D - 3) = 360
? (D + 4) x ( (360 - 3D)/D ) = 360
? (D + 4) x ( (360 - 3D) ) = 360 x D
? (D + 4) x (360 - 3D) = 360 x D
After multiplication by algebra law,
? 360 x D - 3D x D + 4 x 360 - 4 x 3D = 360D
? 360 x D - 3D
? - 3
D
? - 3
D
? 3
D
?
D
?
D
?
D
?
D(
D + 24) - 20(
D + 24) = 0
? (
D + 24) (
D - 20) = 0
Either (
D + 24) = 0 or (
D - 20) = 0
So
D = - 24 or
D = 20
But days cannot be negative so D = 20 days.
Method 2 to solve this question.
Let us assume the original day of tour is d days.
Given that his tour is extended for 4 days
Hence daily expenses per days = 360/(d + 4)
Therefore, According to question,
360/d - 360/(d + 4) = 3
? (360(d + 4) - 360d)/d x (d + 4) = 3
? (360(d + 4) - 360d)/d x (d + 4) = 3
? 360(d + 4) - 360d = 3d x (d + 4)
? 360d + 1440 ? 360d = 3(d
2 + 4d)
? 1440 = 3d
2 + 12d
? 3d
2 + 12d ? 1440 = 0
? d
2 + 4d ? 480 = 0
? d
2 + 24d ? 20d ? 480 = 0
? d(d + 24) ? 20(d + 24) = 0
? (d + 24)(d ? 20) = 0
? (d + 24) = 0 or (d ? 20) = 0
? d = ?24 or d = 20
Since days cannot be negative, d = 20
Hence his original duration of the tour is 20 days.
Correct Answer: 127
Explanation:
For n =1
76n - 66n = 76 - 66
? ( 73 )2 - ( 63 )2
? ( 73 - 63 )( 73 + 63 )
= ( 343 - 216 )( 343 + 216 )
= 127 x 559
? it is clearly divisible by 127.
Correct Answer: 46 minutes 12 seconds
Explanation:
L.C.M. of 252, 308 and 198 = 2772 seconds
= 46 × 60 + 12 = 46 min 12 seconds.
.
Correct Answer: divisible by 24 always
Explanation:
Solving the question by taking two odd numbers greater than 1 i.e. 3 and 5,
for n =3, n( n2 -1 ) = 3( 9 - 1) = 24
for n = 5 n( n2 -1 ) = 5( 25 - 1) = 120
Using option we find that both the number are divisible by 24.
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