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- Question
- 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
- Correct Answer
- 60 years, 32 years
ExplanationMethod 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 - 1. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Options- A. 2 : 3
- B. 4 : 3
- C. 6 : 7
- D. 9 : 16 Discuss
- 2. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options- A. 40 sec
- B. 42 sec
- C. 45 sec
- D. 48 sec Discuss
- 3. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Options- A. 45 m
- B. 50 m
- C. 54 m
- D. 72 m Discuss
- 4. If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be:
Options- A. 1
- B. 2
- C. 3
- D. 4
- E. None of these Discuss
- 5. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:
Options- A. 553681
- B. 555181
- C. 555681
- D. 556581 Discuss
- 6. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
Options- A. 3
- B. 13
- C. 23
- D. 33 Discuss
- 7. (17)3.5 x (17)? = 178
Options- A. 2.29
- B. 2.75
- C. 4.25
- D. 4.5 Discuss
- 8. The number of odd days in a leap year is?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 9. 16, 4, 2, 1.5, 1.75, 1.875
Options- A. 1.875
- B. 1.75
- C. 1.5
- D. 2 Discuss
- 10. In a circus there was a leopard and a tiger walking in the two different rings of same radii. There I observed that when leopard moved 3 steps, tiger moved 5 steps in the same time,but the distance traversed by leopard in 5 step is equal to the distance traversed by tiger in 4 steps. what is the number of rounds that a leopard made when tiger completed 100 rounds?
Options- A. 120
- B. 48
- C. 75
- D. none of these Discuss
More questions
Correct Answer: 4 : 3
Explanation:
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
Correct Answer: 40 sec
Explanation:
| Formula for converting from km/hr to m/s: X km/hr = | ❨ | X x | 5 | ❩ | m/s. |
| 18 |
| Therefore, Speed = | ❨ | 45 x | 5 | ❩m/sec | = | 25 | m/sec. |
| 18 | 2 |
Total distance to be covered = (360 + 140) m = 500 m.
| Formula for finding Time = | ❨ | Distance | ❩ |
| Speed |
| ∴ Required time = | ❨ | 500 x 2 | ❩sec | = 40 sec. |
| 25 |
Correct Answer: 50 m
Explanation:
| 2 kmph = | ❨ | 2 x | 5 | ❩ | m/sec = | 5 | m/sec. |
| 18 | 9 |
| 4 kmph = | ❨ | 4 x | 5 | ❩ | m/sec = | 10 | m/sec. |
| 18 | 9 |
Let the length of the train be x metres and its speed by y m/sec.
| Then, | ❨ | x | ❩ | = 9 and | ❨ | x | ❩ | = 10. |
|
|
∴ 9y - 5 = x and 10(9y - 10) = 9x
⟹ 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
∴ Length of the train is 50 m.
Correct Answer: 3
Explanation:
Then number 6 x 2 must be divisible by 8.
∴ x = 3, as 632 is divisible 8.
Correct Answer: 555681
Explanation:
987 = 3 x 7 x 47
So, the required number must be divisible by each one of 3, 7, 47
553681 → (Sum of digits = 28, not divisible by 3)
555181 → (Sum of digits = 25, not divisible by 3)
555681 is divisible by 3, 7, 47.
Correct Answer: 23
Explanation:
L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
∴ Number to be added = (60 - 37) = 23.
Correct Answer: 4.5
Explanation:
Let (17) 3.5 x (17) x = 17 8
Then, (17)3.5 + x = 178.
∴ 3.5 + x = 8
⟹ x = (8 - 3.5)
⟹ x = 4.5
Correct Answer: 2
Explanation:
A leap year has (52 week + 2 days).
So, the number of odd days in a leap year is 2
Correct Answer: 1.75
Explanation:
Series pattern
16 x 0.25 = 4,
4 x 0.50 = 2,
2 x 0.75 =1.5,
1.5 x 1.00 = 1.5
Should come in place of 1.75
1.5 x 1.25 = 1.875
Clearly, 1.75 is wrong and will be replaced by 1.5
Correct Answer: 48
Explanation:
The ratio of speeds = The ratio of distances, when time is constant
? The ratio of distance covered by leopard to the tiger = 12 : 25
Again, ratio of rounds made by leopard to the tiger = 12 : 25
hence, leopard makes 48 rounds, when tiger makes 100 rounds
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