66. A and B go cycling in the same direction with speeds of 6 km/hr and 12 km/hr. A car from behind passes them in 9 and 10 seconds respectively. What is the speed of the car?

A. 22 km/hr
B. 33 km/hr
C. 66 km/hr
D. 44 km/hr
✅ The correct answer is option C. 66 km/hr.
The relative speed of A and B is 6 km/hr = 1.67 m/s

As the car passes A after 10s, the distance between A and B after 10s (i.e. at 11th second) is the distance covered by car in 1 second.

Therefore, at t = 11, d = 1.67 * 11

d = 18.33 m

v = d/t = 18.33/1 = 18.33m/s

v = 66 km/hr

67. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage iikcrease in the number of boys and girls be 20% and 10% respectively, what will be the new ratio ?

A. 8 : 9
B. 17 : 18
C. 21 : 22
D. Cannot be determined
✅ The correct answer is option C. 21 : 22.
Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x), i . e . ( 120/100 X 7x ) and ( 110/100 X 8x ) i . e . 42x/5 and 44x/5 Required ratio = 42x/5 : 44x/5 = 21 : 22