Let 'M' be the maximum marks in the examination.
Therefore, Madhu got 32% of M = 32M/100 = 0.32M
And Kumar got 42% of M = 42M/100 = 0.42M.
In terms of the maximum marks Kumar got 0.42M - 0.32M = 0.1M more than Madhu. ---- (1)
The problem however, states that Kumar got 16 marks more than the cut-off mark and Madhu got 8 marks less than the cut-off mark. Therefore, Kumar has got 16 + 8 = 24 marks more than Madhu. ---- (2)
Now, Equating (1) and (2), we get
0.1M = 24 => M = 24/0.1 = 240
'M' is the maximum mark and is equal to 240 marks.
We know that Madhu got 32% of the maximum marks.
Therefore, Madhu got 32 x 240/100 = 76.8 marks.
We also know that Madhu got 8 marks less than the cut-off marks.
Therefore, the cut-off marks will be 8 marks more than what Madhu got
= 76.8 + 8 = 84.8.
The favourable cases are (1, 3), (2, 4) , (3, 5), (4, 6) and (1, 4), (2, 5), (3, 6) and their reversed cases like (3, 1), (4, 2), (5, 3)...
Total number of favourable cases = 2 x 7
? Required Probability P(E) = 14/36 = 7/18
Shantanu's 1 day's work = 1/2
Manu's 1 day's work =1/10
Shantanu's share : Manu's share =(1/12) : (1/10)
= (5/60) : (6/60)
= 5 : 6
Cost of coffee powder used in one cup = 20/10 = ? 2
Cost of milk used in one cup = (30/1000) x 200 = ? 6
? Cost of each cup coffee = 2 + 6 = ? 8
To gain 25% profit, sale price of each cup of coffee = 125% of 8 = ? 10
Let the sugar sold at 8% gain = P
? Sugar sold at 18% gain = (1000 - P)
Let CP of sugar = ? Q per kg
Total CP = ? 1000 x Q
? [(108/100) x PQ)] + [(118/100) x (1000 - P) x Q]
= (114/100) x 1000 Q
? 108PQ + 118000Q - 118PQ = 114000Q
? 10P = 4000
? P = 400
? Quantity sold at 18% profit = 1000 - 400 = 600 kg
In each number except 751, the difference of third and first digit is the middle one .
The pattern is 23, 33, 43, 53, 63, 73.
But 100 is not a perfect cube
Pattern is 1st x 2nd = 3rd; 2nd x 3rd = 4th, 3rd x 4th = 5th. But 4th x 5th = 50 x 500 = 25000 ? 5000 = 6th.
Prime numbers 2, 3, 5, 7, 11, 13 have successively been subtracted. So, 100 is wrong. It must be (108 - 11) i.e., 97.
There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22). Increasing by 3 and 5 respectively.
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