B's 9 day's work = 9 x (1/12) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/4 work is done by A in = 20 x (1/4) = 5 days.
Required time taken by B to complete the work = xy / x - y
[Here x = 12 and y = 8]
? required time = (12 x 8) / (12 - 8) = 96/4 = 24 days
Out of 15 fruits, 7 are alike of one kind, 5 are alike of a second kind and 3 are alike of a third kind.
Hence, the required number of ways = [ (7+1) (5+1) (3+1) -1] =191
Required time taken to complete the work by both together = x y / x + y
(Here x = 8 and y = 4)
? Required time = (8 x 4)/(8 + 4) = 32/12 = 22/3 hours
Let last digit is 2
when second last digit is 4 remaining 4 digits can be filled in 120 ways, similarly second last digit is 6 remained 4 digits can be filled in 120 ways.
so for last digit = 2, total numbers=240
Similarly for 4 and 6
When last digit = 4, total no. of ways =240
and last digit = 6, total no. of ways =240
so total of 720 even numbers are possible.
Given word is THERAPY.
Number of letters in the given word = 7
Number of vowels in the given word = 2 = A & E
Required number of different ways, the letters of the word THERAPY arranged such that vowels always come together is
6! x 2! = 720 x 2 = 1440.
Number of cards in a pack of cards = 52
Number of black cards = 26
Number of king cards = 4 (2 Red, 2 Black)
Required, the probability that if a card is drawn either card is black or a king =
15! - 14! - 13!
= (15 × 14 × 13!) - (14 × 13!) - (13!)
= 13! (15 × 14 - 14 - 1)
= 13! (15 × 14 - 15)
= 13! x 15 (14 - 1)
= 15 × 13 × 13!
Required number of 5 digit numbers can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits are
5 x 4 x 3 x 2 x 1 = 120.
A's 1 day's work = 1/12
B's 1 day's work = 1/12 + 60% of 1/12 = 1/12 x 160/100 = 2/15
? B can do the work in 15/2 days = 71/2 days.
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