The average runs scored by a cricketer is 42 innings, is 30. The difference between his maximum and minimum scores in an inning is 100. If these two innings are not taken into consideration, then the average score of remaining 40 inning is 28. Calculate the maximum runs scored by him in an innings?

According to the question
(P + T + R) / 3 = 54¹/₃
? P + T + R = (163/3) x 3
? P + T + R = 163 ............(i)
Also (T + F + G)/3 = 53
? T + G + F = 159 ..........(ii)
Clearly, from the two Eqs. (i) and (ii), the problem cannot be solved.

Let temperature on sunday be x° C.
(20° + 18.6° + 17° + 21.4° + 19° + 19.8° + x) / 7 = 19.5°
? 115.8 + x = 19.5 x 7
? x = 136.5 - 11.58
? x = 20.7°C

Here, P = 9 km/h, Q = 25 km/h, R = 30 km
x = 3 km/h, y = 5 km/h and z = 10 km/h
? Required average speed
= [P + Q + R] / [(P/x) + (Q/y) + (R/z)] = [9+25 + 30] / [(9/3) + (25/5) + (30/10)]
= 64/(3 + 5 + 3)
= 64/11
= 5⁹/_{11 km/h}

According to the average speed formula,
P = 1/4, Q =3/5, R = 3/20
x = 8 km/h, y = 6 km/h, z = 10km/h
? Required average speed = 1 / [(P/x) + (Q/y) + (R/z)]
=1 / [(1/32) + (1/10) + (3/200)]
= 1/[(25 + 80 + 12)/800]
= 800/117
= 6.83 km/h

Required average rate of reading
= 2AB / (A + B) = 2 x 60 x 40 / (60 + 40)
= (2 x 60 x 40)/100 = 48 page/h

Distance between Raipur and Somgarh
= Average speed x Time
= 69 x 35/60= 161/4 km
New speed = (69 + 36) km/h = 105 km/h
? Time = Distance/ Speed = 161/4 x 105 h
= 161 x 60/4 x 105min = 23 min

Let average after 10th innings = x.
According to the question.
10x + 216 = 11(x +12)
? x = 216 - 132 = 84
? New average = 84 + 12 = 96

Let x be the number of wickets taken till the last match
According to the question,
(12.4 x + 26) = 12(x + 5)
? 12.4 x + 26 = 12x + 60
? 0.4 x = 34
? x = 34/0.4 = 85

Let the ages of mother, father and boys be M, F, B₁ and B₂, respectively.
The total age of four member
= 19 x 4
= 76 yr.

Given (B₁ + B₁)/2 = 11/2
? B₁ + B₂ = 11
M + F + B₁ + B₂ = 76 - 11
? M + F = 65 .......(i)

According to the question,
(B₁ + B₂ + F) / 3 = (B₁ + B₂ + M) / 3 + 3
? B₁ + B₂ + F) = B₁ + B₂ + M + 9
? F = M + 9
? F - M = 9 ............. (ii)

From Eqs (i) and (ii), we get
F = 37 yr and M = 28 yr

Let money of C be ? N.

According to the question
Total money of B = N + N x 50%
= N + 50N/100 = 3N/2

Total money of A = 2 x 3N/2 = 3N

Average money of three persons = 12000
? Total money of three = 12000 x 3
? 3N + (3N/2) + N = 12000 x 3
? (6N + 3N + 2N)/2 = 36000
? N = (36000 x 2)/11 = 72000/11

Now, money of A = 3N = (3 x 72000)/11
= ? 216000/11