Quantitative Aptitude - Arithmetic Ability Questions

First we need to choose two vowels 3C2 and then three consonants 5C3. Now that we have 5 letters required to make the word,arrange them in 5! ways.

So,3C2*5C3*5! = 3600

The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.

 Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where 0≤x,y,z≤9.

Let us first count the numbers in which 8 occurs exactly once.

Since 8 can occur atone place in 3C1ways. There are 3 x 9 x 9 such numbers.

Next, 8 can occur in exactly two places in 3C2×9 such numbers. Lastly, 8 can occur in all three digits in one number only.

Hence, the number of times 8 occur is 

 1×3×92+2×3×9+3×1 = 300

Number of persons * days = work  

20 * 7 = 140 man- days 

Now,  x * 28  = 140 men- days

=> x =5         

Therefore in second case the required number of person is 5.

Second method:

Since work is constant, therefore  M1 x D1= M2 x D2

20 x 7 = M2 x 28

=> M2 = 5 

1 boy's 1 day work = 1/70

1 girl's 1 day work = 1/140

(5 boys + 10 girls)'s 1 day work = (5/70 + 10/140) = (1/14 + 1/14) = 1/7

5 boys and 10 girls will complete the work in 7 days.

1/K + 1/L + 1/M = 1/8 (Given)
Also given that K = 2L and L = 2M
=> 1/2L + 1/L + 2/L = 1/8
=> (1 + 2 + 4)/2L = 1/8
=> 2L/7 = 8
=> L = 28 hours.

2(l+b)/b = 5/1 

=> 2l + 2b = 5b  

=> 3b = 2l  

=> b =(2/3) x l

 Then, Area = 216 sq.cm 

l x b = 216  

=> l x [(2/3)x l] =216  

=> l x l = 324 

=> l = 18 cm.

1st day the girl read = 40%

2nd day she read = 34 %

Remaining percentage of book = 100% - (40% +34%) = 26%

But given last two days she read equal number of pages

=> Each day she read 26%/2 = 13%

Last day she read 52 pages = 13%

13% = 52

1% = 4

=> 100% = 400

Total pages in the book is 400.