Arranging letters in alphabetical order: ACELPSTUUY, only U is repeated (2 U’s)
Words starting with Alphabet A = 9!/2!
Words starting with Alphabet C = 9!/2!
Words starting with Alphabet EA = 8!/2!
Words starting with Alphabet EC = 8!/2!
Words starting with Alphabet EL = 8!/2!
Words starting with Alphabet EP = 8!/2!
Words starting with Alphabet ES = 8!/2!
Words starting with Alphabet ET = 8!/2!
Words starting with Alphabet EUA = 7!
Words starting with EUCALP= 4!
Words starting with EUCALS= 4!
Words starting with EUCALT= 4!
Words starting with EUCALU= 4!
Words starting with EUCALYPS = 2!
Words starting with Alphabet EUCALYPTS= 1
And next word is EUCALYPTUS
Sum of all words = 2*9!/2! + 6*8!/2! + 7! + 4*4! + 2! +1 = 488980
First 10 Prime Nos.:
2 3 5 7 11 13 17 19 23 29
Nth term of Series is formed by multiplication of nth*(n+1)th prime numbers
2*3, 3*5, 5*7 .....and so on
9th Term would be = 23*29 = 667
Ram and Rahim each working alone can do a work in 22 and 33 days respectively. They started the work together but one day Rahim left the work in between and Ram finished the remaining work in 11 days. For how many days Rahim had worked for?
OPtion
1) 6 days
2) 6.1 days
3) 6.2 days
4) 6.3 days
5) 6.4 days
6) 6.5 days
7) 6.6 days
8) 6.7 days
9) 6.8 days
10)6.9 days
Solution
Ram's one day's work=1/22
Rahim's one day's work=1/33
In 11 days Ram worked =11/22 = 1/2
So Ram and Rahim together completed 1/2 work
(Ram+Rahim)'s one day's work= (3+2)/66 = 5/66
5/66 work is done by Ram and Rahim together in 1 day
1 work is done by Ram and Rahim together in 66/5 days
1/2 work is by Ram and Rahim together in 1/2*(66/5) days = 33/5 days = 6.6 days
Option 7)
No alphabets are repeated, arranging letters in alphabetical order: BEGHINORU
Words starting with Alphabet B = 8!
Words starting with Alphabet E = 8!
Words starting with Alphabet G = 8!
Words starting with Alphabet H = 8!
Words starting with Alphabet I = 8!
Words starting with NB = 7!
Words starting with NEB = 6!
Words starting with NEG = 6!
Words starting with NEH = 6!
Words starting with NEIB = 5!
Words starting with NEIGB = 4!
Words starting with Alphabet NEIGHBOR = 1
And next word is NEIGHBOUR
Sum of all words = 5*8! + 7! + 3*6! + 5! + 4! +2 = 208946
Option 6)
I bought 5 Rasgullas, 7 Ladoos and 4 Samosas. Preeti bought 6 Rasgullas, 8 Samosas and 14 Ladoos for an amount which was half more than what I had paid.
What percent of the total amount paid by me was paid for the Rasgullas?
Assume R is Cost of one Rasgulla, L is cost of one Ladoo& S is cost of one Samosa
Let total cost of 5 Rasgullas, 7 Ladoos and 4 Samosas be X
5R+7L+4S=X -> Equation (i)
Preeti has bought 6 Rasgullas, 8 Samosas and 14 Ladoos at 1.5X cost (half more than mine)
So, 6R+14L+8S=1.5X -> Equation (ii)
Multiplying Equation (i) by 2 and subtracting 2nd equation from it:
10R+14L+8S=2X
06R+14L+8S=1.5X
--------------------------------
4R = 0.5X
=> R = 0.5X/4
Total amount paid by me for Rasgulla = 5R= (0.5X/4) * 5 = 2.5X/4
Percent of the total amount paid by me for the Rasgulla = {(2.5X/4)/X}* 100 = 62.5%