2³+ 0.5 = 8.5

3³– 0.5 = 26.5

4³ + 0.5 = 64.5

5³ – 0.5 = 124.5 (not 125.5)

6³ + 0.5 = 216.5

7³ – 0.5 = 342.5

8³ + 0.5 = 512.5

33   39   57   87   129   183

Difference is

+6   +18   +30   +42   + 54

Difference of difference is

+12    +12   +12    +12

1 + 2² = 5

2 + 3² = 11

3 + 4² = 19

4 + 5² = 29 (not 32)

5 + 6² = 41

6 + 7² = 55

10 x 1/2 + 10 = 15

20 x 1 + 20= 40

30 x 3/2 + 30 = 75

40 x 2 + 40 = 120

50 x 5/2 + 50 = 175 (not 155)

60 x 3 + 60 = 240

70 x 7/2 + 70 = 315

2 x 2² + 0.5 = 8.5

3 x 3² + 1 = 28

4 x 4² + 1.5 = 65.5

5 x 5² + 2 = 127

6 x 6² + 2.5 = 218.5 (not 218)

7 x 7² + 3 = 346

8 x 8² + 3.5 = 515.5

Let, CP of 42 articles is Rs. 100

SP of 30 articles = CP of 42 articles = 100

SP of 1 article = 100/30

And, SP of 42 articles = 42/30*100=140

Profit% = (140 – 100)/100 x 100 = 40%

Efficiency of A = 1/25

Efficiency of B = 1/30

(A+B) worked for 5 days = (1/25+1/30) x 5 = 11/30 units.

Remaining work left = 1- 11/30 = 19/30 units.

B will complete the remaining work in = (19/30) ÷ (1/30) = 19 days

A = 35000

B = 20000

C = 34000

A     :        B         :      C

35000 x 12 : 20000 x 12 : 34000 x 12

35  :       20        :      34

Now,

(35 + 20 + 34) = 89’s = 712000

35’s = 712000/89 x 35 = 280000

34’s = 712000/89 x 34 = 272000

So, sum of profit of A & C = 280000 + 272000 = Rs.552000

Speed of the boat = a

Speed of the stream = b

 Downstream Speed = a + b = 72/2 = 36 km/hr  ......(i)

Upstream Speed = a – b = (1 – 200/300) x 36 = 12 km/hr  ........(ii)

Solving the eq. (i) and (ii) we get,

2a = 48

a = 24 km/hr and b = 12 km/hr.

Area of the triangle = ½ x base x height = 1/2 x 13 x 12 = 78 cm²

Area of the circle = 2/3 x 78 = 2 x 26 = 52 cm²

22/7 x r² = 52

r = (52 x 7)/22 = √16.54 = 4.06 = 4cm approx.