A car reached Raipur from Somgarh in 35 min With an average speed of 69 km/h. If the average speed is increased by 36 km/h, how much time will it take to cover the same distance?

Let the minimum score = x
? Maximum score = x + 100
? x + (x + 100) = 30 x 42 - 40 x 28
? 2x + 100 = 1260 - 1120 = 140
? 2x = 140 - 100 = 40
? x = 20
Hence, the maximum score = x + 100
= 20 + 100 = 120

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

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

Let the required runs be N.

According to the question,
(80 x 99 + N) / 80 = 100
? 7920 + N = 8000
? N = 80