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- Question
Jay wants to buy a total of 100 plants using exactly a sum of Rs 1000. He can buy Rose plants at Rs 20 per plant or marigold or Sun flower plants at Rs 5 and Re 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?
Options- A. 3
- B. 6
- C. 4
- D. 2
- Correct Answer
- 3
ExplanationLet the number of Rose plants be ?a?.
Let number of marigold plants be ?b?.
Let the number of Sunflower plants be ?c?.
20a+5b+1c=1000; a+b+c=100Solving the above two equations by eliminating c,
19a+4b=900b = (900-19a)/4
b = 225 - 19a/4----------(1)
b being the number of plants, is a positive integer, and is less than 99, as each of the other two types have at least one plant in the combination i.e .:0 < b < 99--------(2)
Substituting (1) in (2),0 < 225 - 19a/4 < 99
225 < -19a/4 < (99 -225)
=> 4 x 225 > 19a > 126 x 4
=> 900/19 > a > 505
a is the integer between 47 and 27 ----------(3)
From (1), it is clear, a should be multiple of 4.
Hence possible values of a are (28,32,36,40,44)
For a=28 and 32, a+b>100
For all other values of a, we get the desired solution:
a=36,b=54,c=10
a=40,b=35,c=25
a=44,b=16,c=40
Three solutions are possible. - 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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