Let the number be 4N, 5N and 6N
Then, 4N + 5N + 6N/3 = 25
or 15N = 75
or N = 5
Then largest number = 6N = 6 x 5 = 30
There are 13 hearts and 3 more kings
? P(heart or a king) = (13 + 3)/52 = 4/13
? P (neither a heart nor a king) = 1 - 4/13 = 9/13
Total number of caps = 12
? n(S) = 12C3 = 220
n(E1) = Out of 4 red caps, number of ways to pick 2 caps = 4C2 = 6
n(E2) = Out of 5 green caps
Number of ways to pick one cap = 5C1 = 5
P(E) = n(E1) x n(E2)/n(S) = (6 x 5)/220 = 3/22
Total Number of outcomes = 10C3 = 120
Number of outcomes not containing red balls = 5C3 = 10
? Probability that at least one is red = 1 - 10/120 = 11/12
Let length of bridge be L m.
We know, Speed = Distance/Time
According to the question,
90 x 5/18 = 150 + L/26
? 25 x 26 = 150 + L
? 650 = 150 + L
? L = 500 m
Total number of caps = 2 + 4 + 5 + 1 = 12
Total number of outcomes = n(S) = 12 C2 = 66
Favorable number of outcomes = n(E) = 2C2 = 1
? Required probability = 1/66
Ways of selection of two green marbles = 2C2 = 1
Ways of selection of two yellow marbles = 3C2 = 3
So, probability (both are green) = 1/15C2 ....(I)
Probability (both are yellow) = 3/15C2 ....(Ii)
Then, required probability = 1/15C2 + 3/15C2 = 4/ 15C2
= 4/105
? = 3/5 of 4/7 of 7/9 of 425
? ? = 3/5 x 4/7 x 7/9 x 425 = 113.33 = 113
? Loss% = (20/10)2 = (2)2 = 4%
? Total S.P. = Rs. 24000
? Total C.P. = Rs. (100/96) x 24000 = Rs. 25000
? Loss = Rs. 1000
Relative speed of policeman with thief = (10 - 8) = 2 km/h
Now, time taken to cover 100 m with speed of 2 km/h or 2000 m/h
Now, Speed = Distance / Time
? Time = D/S = 100/2000
= 1/20 h or 60/20 min = 3 min
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