Concentration of Acid in the final solution= 52%

The pattern is as follows:

15² + 6 = 231

14² + 5 = 201

13² + 4 = 173

12² + 3 = 147

11² + 2 = 123

10² + 1 = 101

Rajan's present age = 17 + 4 = 21 years

Rohini's present age = 21 - 3 = 18 years

Mohini's present age = 18 * 2/3 = 12 years

Difference in principal = 6500-6000 = 500

i.e., Simple Interest on Rs.500 will be Rs.25

500 x 5 x T/100 = 25 or T = 1 year

Let, Mugdha's speed = x km/hr.

Then Bimal's speed = 3x km/hr.

Then Amal's speed = 6x km/hr.

So, ratio of speeds of Amal: Bimal: Mugdha = 6x : 3x : x = 6 : 3 : 1

Ratio of times taken = 1/6 : 1/3 : 1 = 1:2:6

Therefore, 6:1 = 78: t, where t is time taken by Amal finish the journey

Or, 6t = 78

So, t = 13 min.

The pattern is as follows:

6 + 14 x 1 = 20

20 + 14 x 2 = 48

48 + 14 x 3 = 90

90 + 14 x 4 = 146

146 + 14 x 5 = 216

Total number of patients suffering Cancer or obesity = 150

Total number of patients = 270

Percentage = [(150/270) X 100] = 55.55%

Shortcut

=> Net change= ±a ±b ±ab/100

=> a = +10

=> b = -10

\ = 10-10-10*10/100

= -1%

\ decrease by 1%

Long method

Let initial area = xy

Area after change = (90x/100)*(110y/100)

= 99xy/100

\ Change = (99xy/100) - xy

= -xy/100

=> % change = ( - xy/100)/xy*100= -1%

The pattern is as follows:

8³ - 4 = 508

7³ - 5 = 338

6³ - 6 = 210

5³ - 7 = 118

4³ - 8 = 56

3³ - 9 = 18

Total number of students = 1200

Boys : Girls = 7:5

Number of boys in the school = 7/12 x 1200 = 700

Number of girls in the school = 5/12 x 1200 = 500

Number of boys from village R = 45/100 x 700 = 315

Number of boys from village P = 315 x 80/100 = 252

Number of boys from village Q = (700 - 315 - 252) = 133

Number of girls from village P = ¾ x 252 = 189

Number of girls from village R = 5/7 x 189 = 135

Number of girls from village Q = (500 - 189 - 135) = 176

Number of students from village P = 441

Number of students from village R = 450

Required sum = 441 + 450 = 891