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- Question
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Options- A. 23 years
- B. 24 years
- C. 25 years
- D. None of these
- Correct Answer
- 23 years
Explanation
Let the average age of the whole team by x years.∴ 11x - (26 + 29) = 9(x -1)
⟹ 11x - 9x = 46
⟹ 2x = 46
⟹ x = 23.
So, average age of the team is 23 years.
- 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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