Mathematics

Let the distance be d km. Asghar's time = d/10 + d/9 hours. Rohit's time = 2d/12 = d/6 hours. The difference in time is 10 minutes = 1/6 hour. So, (d/10 + d/9) - (d/6) = 1/6. Solving gives d = 3.75 km or 3750 meters.

A completes 80% of the work in 20 days, so A's 1 day work = 80%/20 = 4% of the work. Remaining work = 20%. A and B together finish this in 3 days, so their 1 day work = 20%/3 ≈ 6.67%. Since A alone does 4% per day, B alone does (6.67% - 4%) = 2.67% per day. Therefore, B alone will complete the work in 100%/2.67% ≈ 37.5 days.

A completes 1/3 of the work in 5 days, so A's work rate is (1/3)/5 = 1/15 of the work per day. B completes 2/5 of the work in 10 days, so B's work rate is (2/5)/10 = 1/25 of the work per day. Together, their combined work rate is 1/15 + 1/25 = (5 + 3)/75 = 8/75 of the work per day. Therefore, the total time for both working together to complete the entire work is the reciprocal of their combined rate, which is 75/8 days (9.375 days). Among the options, 75/8 days corresponds exactly to option A, making it the correct answer.

Atif and Bilal start 110 km apart and cycle towards each other. Their speeds are in the ratio 6:5, so the total parts are 6 + 5 = 11. The distance each covers before meeting is proportional to their speeds. Therefore, Atif's share of the distance is (6/11) × 110 = 60 km. This matches option D. The original correct answer A (66 km) is incorrect based on the ratio calculation.

Tap X fills 1/10 of the tank per hour, and tap Y fills 1/15 of the tank per hour. Together, they fill 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 of the tank per hour. Therefore, the time taken to fill the tank when both taps are opened together is the reciprocal of 1/6, which is 6 hours. Hence, the correct answer is D (6 hrs).

Each machine produces 270 ÷ 6 = 45 bottles per minute. Therefore, 10 machines produce 10 × 45 = 450 bottles per minute. In 4 minutes, they produce 450 × 4 = 1800 bottles.

The man normally walks at 6 kmph and reaches his destination at 9:00 am. Walking slower, he reaches at 10:00 am, which is 1 hour later. The distance to the destination is 12 km. At 6 kmph, the time taken is 12 km ÷ 6 kmph = 2 hours. Walking slower, the time taken is 3 hours (2 + 1). Therefore, the slower speed is distance ÷ time = 12 km ÷ 3 hours = 4 kmph. Hence, the correct answer is 4 kmph, which corresponds to option B.

A's work rate is 1/10 per day and B's is 1/15 per day. Together, their combined rate is 1/10 + 1/15 = 1/6 per day. The ratio of A's work to B's work is (1/10) : (1/15) = 3 : 2. Therefore, A's share of the Rs.75 wages is (3/5) × 75 = Rs.45.

A and B together complete 1/30 of the work per day. In 20 days, they complete 20/30 = 2/3 of the work. The remaining 1/3 is done by A alone in 20 days, so A's one day work is (1/3)/20 = 1/60. Therefore, A alone can finish the work in 60 days.

P's work rate is 1/20 per day, Q's is 1/30 per day, and R's is 1/60 per day. For two days, only P works, completing 2*(1/20) = 1/10 of the work. On every third day, P, Q, and R work together, completing (1/20 + 1/30 + 1/60) = 1/10 of the work. Thus, every 3 days, they complete 1/10 + 1/10 = 1/5 of the work. To complete the entire work, it takes 5 cycles of 3 days each, totaling 15 days. Therefore, the correct answer is 15 days (option C).