Quantitative Aptitude - Arithmetic Ability Questions

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.

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.

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.

 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

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.

From statement (A),

20b = (1/2) × b × h

h = 40 cm.