Let the sum lent at 5% = P
? Sum lent at 8% = (1550 - P)
Then, [(P x 5 x 4)/100] + [{(1550 - P) x 8 x 4}/100] = 400
? 20P - 32P + 1550 x 32 = 40000
? - 12P + 49600 = 40000
? - 12P = - 9600
? p = ? 800
Sum lent at 8% = 1550 - 800 = ? 750
? Required ratio = 800 : 750 = 16 : 15
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
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 |
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.
∴ x = 3, as 632 is divisible 8.
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.
On dividing 2497 by 60, the remainder is 37.
∴ Number to be added = (60 - 37) = 23.
Then, (17)3.5 + x = 178.
∴ 3.5 + x = 8
⟹ x = (8 - 3.5)
⟹ x = 4.5
A leap year has (52 week + 2 days).
So, the number of odd days in a leap year is 2
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
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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