BANK & INSURANCE (SPEED TIME AND DISTANCE) PART 3

From quantity I,
A = 1/36
A + B = 1/24 days
B = 1/24 - 1/36
B = 1/72

C = 7/120 - 1/24 = 1/60

LCM of 36, 72, 60 = 1080

Work done by A alone in a day = 1080/36 = 30 units
Work done by B alone in a day = 1080/72 = 15 units
Work done by C alone in a day = 1080/60 = 18 units

After three days = 30 + 15 + 18 = 63 units of work is completed

After 51 days = 63 × 17 = 1071

A alone complete 9 units of work in 9/30 = 3/10 days

Total time = 51 (3/10) days

From quantity II,
A = 100/60 × 54 = 90 days
B = 2/1 × 30 = 60
C = 90

{(x + 10)/90} + {(x + 10)/60} + {x/90} = 1

2x + 20 + 3x + 30 + 2x = 180

7x = 130

x = 130/7

Total time = 10 + 130/7 = 28 (4/7) days

Quantity I > quantity II

Let the speed of the car B = 5x
And the speed of the car A = 5x × 80/100 = 4x

5x - 4x = 13
x = 13

The speed of the car A = 4 × 13 = 52 km/hr
The speed of the car B = 5 × 13 = 65 km/hr

The distance between Chennai to Delhi = (52 + 65) × 7 = 819 km

Ratio of speed of P and Q = 3:5
Let the total distance is 5 km

So, total time taken by P to cover whole distance
= 20% × 5 / 3a + 80% × 5 / 5a = 17/15a

Total time taken by Q to cover whole distance
= 20% × 5 / 5a + 80% × 5 / 3a = 23/15a

Required ratio = 23/15a : 17/15a = 23:17
Hence answer is option D

Distance between BC is 40% more than AB, So ratio of distance between AB and BC = 5:7

Speed of P is thrice that of Q while traveling from A to B.
Speed of P and Q = 3b : b

Time taken by P to travel from A to B = 5a/3b
Time taken by Q to travel from A to B = 5a/b

Speed of Q is thrice of P while traveling from B to C.
Time taken by P to travel from B to C = 7a/b
Time taken by Q to travel from B to C = 7a/3b

Ratio of time taken by P and Q respectively = (5a/3b + 7a/b) : (5a/b + 7a/3b)
= (5a/3b + 7a/b) : (5a/b + 7a/3b) = 13:11

Hence the answer is option C

Difference = 2960 - 2320 = 640
Time taken by Sita = 1/8 × 160 = 20 hours
Time taken by Buvanesh = 10 + 20 = 30 hours
Time taken by Diya = 100/60 × 30 = 50 hours
Time taken by Anil = 2x
Time taken by Ezhanth = 3x

2x + 3x + 20 + 30 + 50 = 160
5x = 60
x = 12

Time taken by Anil = 2 × 12 = 24 hours
Time taken by Ezhanth = 3 × 12 = 36 hours

Distance covered by Anil = 840 km
Speed of Anil = 840/24 = 35 kmph

Distance covered by Ezhanth = 9/7 × 840 = 1080
Speed of Ezhanth = 1080/36 = 30 kmph

Distance covered by sita = 1080 - 580 = 500 km
Speed of Sita = 500/20 = 25 kmph: Distance covered by Buvanesh = 30 × 20 = 600 km

Distance covered by Bhuvanesh and Diya
= 3320 - (840 + 1080 + 500) = 900

Distance covered by Diya = 900 × 5/9 = 500
Required speed = 500/50 = 10 kmph

Speed of Buvanesh = 6 × 6 = 36 kmph
Speed of Diya = 7 × 6 = 42 kmph

Distance covered by Buvanesh = 36 × 30 = 1080
Distance covered by Diya = 42 × 50 = 2100

Required speed = (840 + 1080 + 1080 + 2100 + 500)/160 = 35 kmph

The speed of train P on Monday = Distance/Time
= 450/9 = 50 km/hr

The average speed of train P on Monday and Tuesday = 60 km/hr

Average speed = 2 × x × y / (x + y) = 60
2 × 50 × y / (50 + y) = 60

100y = 3000 + 60y
40y = 3000
y = 75 km/hr

The speed of train P on Tuesday = 75 Km/hr

The time taken to reach the destination by train P on Monday and Tuesday is same

The total distance travelled by train P on Tuesday
=> Speed × Time = 75 × 9 = 675 Km