Given there are 9 flavours of ice creams.
Each child takes the combination of two flavours and no two children will have the same combination
This can be done by ways i.e children.
Number of children= = 9 x 8 / 1x 2 = 36.
Let x km . be covered in y hrs.
then, 1st speed = (x / y) km/hr.
2nd speed = [(x/2) / 2y)] km/hr.
= (x/4y) km/hr.
? Ratio of speed = x/y : x/4y = 1 :1/4 = 4: 1
Speed of the train = (36 x 5)/18 = 10 m/sec.
Distance = (Time x Speed ) = (8 x 10 ) = 80 meters
? Length of the train = 80 meters
Relative speed = | = (45 + 30) km/hr | |||||||
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We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
∴ Required time = | ❨ | 500 x | 6 | ❩ | = 24 sec. |
125 |
= | ❨ | 36 x | 5 | ❩m/sec |
18 |
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
Relative speed | = (x + 50) km/hr | |||||||
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Distance covered = (108 + 112) = 220 m.
∴ | 220 | = 6 | ||
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⟹ 250 + 5x = 660
⟹ x = 82 km/hr.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
∴ 20x + 25(x - 1) = 110
⟹ 45x = 135
⟹ x = 3.
So, they meet at 10 a.m.
Relative speed = | = (45 + 30) km/hr | |||||||
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We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
∴ Required time = | ❨ | 500 x | 6 | ❩ | = 24 sec. |
125 |
⟹ x = | ❨ | 18700 x 115 | ❩ | = 25300. |
85 |
Hence, S.P. = Rs. 25,300.
Since 653xy is divisible by 2 and 5 both, so y = 0.
Now, 653x is divisible by 8, so 13x should be divisible by 8.
This happens when x = 6.
∴x + y = (6 + 0) = 6.
(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)
= (4n + 4) x 2
= 8(n + 1), which is divisible by 8.
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