Total speed of car, bus and train = 72 × 3 = 216 Km
Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 Km
Average = 168 / 2 = 84 Km
A : B : C = 90 : 75 : 60
B:C = 75 / 60 = ( 75 x 100?75 ) / ( 60 x 100?75) = 100 / 80
Hence, in a game of 100 points, B can give C(100 - 80)
= 20 points.
A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72.
? While B scores 80, C scores 72.
? While B scores 100, C scores 72 × 100 / 80 = 90.
? B can give C 100 - 90 = 10 points.
Let us assume A cover P meter in the time after which he meets with B.
According to question,
Time taken by A to cover the P distance = Time taken by B to cover the 4200 - P distance.
Use the distance and time formula
P / 500 = (4200 - P ) / 700
Or 700P = 500 x 4200 - 500P
Or 700P + 500P = 500 x 4200
Or 1200P = 500 x 4200
Or 12P = 5 x 4200
Or P = 5 x 4200 / 12
Or P = 5 x 350
Or P = 1750 meters
Required time taken by A to cover 1750 meters = 1750 / 500 = 175/50
Required time taken by A to cover 1750 meters = 3.5 minutes.
Let, times (in sec) taken by A and B to run a Km, be P and Q, respectively.
When B gets a start of 50 m, B runs.
1000 - 50 = 950 m while A runs 1000 m.
? 950 / 100 Q - P = 14,
i.e., 0.95Q - P = 14 ?(1)
and, when B gets a start of 22 seconds, A runs for (Q - 22) seconds, while B runs for Q seconds.
? 1000 - 1000 / P (Q - 22) = 20
i.e., 50Q - 49P = 1100. ?(2)
Multiplying Eq. (1) by 49 and subtract from Eq. (2)
3.45Q = 414
? Q= 120 sec.
? from (1)
? P = 0.95 × 120 - 14 = 100 seconds.
When A makes 5 rounds, B makes 4 rounds.
In order to pass each other, the difference in number of rounds made by each must be one.
Here, A passes B each time, when A makes 5 rounds.
Distance covered by A in 5 rounds = 5 * 400 / 100 × = 2 Km.
In covering 2 Km, A passes B 1 time.
? In covering 5 Km, A passes B
= 5 / 2 = 21?2 times.
Let father's age be 4T and son's age T years.
? 4T x T = 196
? T2 = 49
? T = 7
Father's age after 5 years = (4T + 5) = 33 years
Son's age after 5 years = (T + 5) = 12 years
? Ratio of their ages after 5 years = 33 : 12 = 11 : 4
Let the son's present age be x years
Then, (x + 4) + (4x + 4) = 43
? 5x = 35
? x = 7
? 3x + 5x = 80
? x = 10
Ratio of their ages after 10 years = (3x + 10) : (5x + 10) = 40 : 60 = 2 : 3
Let Ashok's age = 4x years and Pradeep's age = 3x years
From question, 4x + 6 = 26
? x = 5
&ther4; Pradeep's age = 3x = 15 years.
Let Ajay's age 10 years back be x years.
Then Sachin's age 10 years back = 2x years
? 2x + 20 = 40
? x = 10
? Present age of Ajay = x + 10 = 20 years
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