Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

? 137¹/₂% of N = 33
? {(275/2) x N} / 100 = 33
? N = (33 x 2 x 100) / 275 = 24

? (62% of N - 38% of N) =144
? 24% of N = 144
? N = (144 x 100)/24 = 600

Population after 2 years
=8000(1 + 10/100) (1 + 20/100)
= (8000 x 11/10 x 6/5) = 10560

? 540 = H(1 + 20/100)²
? H = (540 x 5/6 x 5/6) = 375 cm

P = 6q. Thus q is less than p by 5q
? q is less than p by = {(6q - q)/6q} x 100%
= ( 5q/6q) x 100 % = 83¹/_{3 %}

Let income = Rs. 100
Then expenditure = Rs. 75 and saving = Rs. 25
New expenditure = 110% of Rs. 75 = Rs. 165 / 2
New saving = Rs. (120 - 165/2) = Rs. 75/2
Increase in saving = Rs. (75/2 - 25) = Rs. 25/2
? Increase% = (25/2) x (1/25) x 100% = 50%

Suppose boys = 3N and girls = 2N
Not adults = (80% of 3N) + (75% of 2N) = (12N/5 + 3N/2) = 39N/10
? Required percentage = (39N/10 / 1/5N) x 100 % = 78%

Let the total number of students be 100
Then, n(A ? B) = n(A) + n(B) - n(A ? B) = (72 + 44 - 100)% = 16%
Now,16% of N = 40
? (16 x N) / 100 = 40
? N = (100 x 40) / 16 = 250

Let the number be N.
Then, error = 5N/2 - 2N/5 = 21N/10
? Error percentage = (21N/10) x (2/5N) x 100 % = 84%

Percentage of car owners = 80%
Percentage of mobile phone owners = 60%
Percentage of people having both car and mobile phone = 55%
Percentage of people having only car = 80 - 55 = 25%
Percentage of people having only mobile phone = 60 - 55 = 5%
Percentage of people having a car or a mobile phone or both = 55% + 25% + 5% = 85%