Circumference of circle = 2πr
Where r = radius of circle

Correct Option: C

Speed in cm/minute = (Speed in km/hr x 1000 x100 )/60
= 47.52x(50/3)
=79200 cm/min

And Circumference of circle = 2πr
=2 x ( 22 / 7 ) x 21
=132

No. of revolutions = ( Speed in cm/minute ) / circumference of circle in cm
=79200 / 132
=600 rpm

New speed = 8/11 of usual speed
New time = 11/8 of usual time
∴ 11/8 of usual time = 11/2 h

Correct Option: C

New speed = 8/11 of usual speed
New time = 11/8 of usual time
∴ 11/8 of usual time = 11/2 h
⇒ Usual time = (11 x 8)/(2 x 11) = 4 h
∴ Time saved = 5¹/₂- 4
= 1¹/₂

Let total distance = x km
According to the question,
x/3 - x/4 = 1/2;

Correct Option: A

Let total distance = x km
According to the question,
x/3 - x/4 = 1/2;
⇒ x/12 = 1/2
∴ x = 6 km

Length of the bridge = Distance travelled by the person in 4 min = Speed x Time
Speed = 54 km/h = 54 x (5/18) = 3 x 5 = 15 m/s
Time = 4 min = 4 x 60 = 240 s

Correct Option: A

Length of the bridge = Distance travelled by the person in 4 min = Speed x Time
Speed = 54 km/h = 54 x (5/18) = 3 x 5 = 15 m/s
Time = 4 min = 4 x 60 = 240 s
∴ Required length = 15 x 240 = 3600 m

Let speed of Kapil in still water = x
and speed of the current= y
∴ Speed upstream = (x - y)
and speed downstream = (x + y)

According to the question,
12/(x - y) - 12/(x + y) = 6
⇒ 6(x² - y²) = 24y
⇒ x² - y² = 4y
⇒ x² = 4y + y² ....(i)

Again, 12/(2x - y) - 12/(2x + y) = 1
⇒ 4x² - y² = 24y
⇒ x² = (24y + y²)/4 ....(ii)

Correct Option: A

Let speed of Kapil in still water = x
and speed of the current= y
∴ Speed upstream = (x - y)
and speed downstream = (x + y)

According to the question,
12/(x - y) - 12/(x + y) = 6
⇒ 6(x² - y²) = 24y
⇒ x² - y² = 4y
⇒ x² = 4y + y² ....(i)

Again, 12/(2x - y) - 12/(2x + y) = 1
⇒ 4x² - y² = 24y
⇒ x² = (24y + y²)/4 ....(ii)

From Eqs. (i) and (ii), we get
4y + y² = (24y + y²)/4
⇒ 16y +4y² = 24y + y²
⇒ 3y² = 8y
∴ y = 8/3 = 2²/₃ mile/h