Mathematics MCQs

Three towns X, Y, and Z are on a river which flows uniformly. Y is equidistant from X and Z. If a boats man rows from X to Y and back in 10 hours and X to Z in 4 hours, find the ratio of speed of the boats man in still water to the speed of the current.

by
A. 2:5
B. 5:3
C. 3:5
D. 1:2
✅ The correct answer is option B. 5:3.
X ———— Y ———— Z

If ‘d’ is the distance between X and Y, then ‘d’ is the distance between Y and Z.

Now the total time for the batsman to row from X to Z is 4 hours. Therefore, time to row from X to Y is 2 hours.

Also the time for the boats man to row from X to Y and back is 10 hours. Hence, time required to row from Y to X is 8 hours.

If, a: speed of boats man in still water

b: speed of the river

d/(a + b) = 2; d/(a – b) = 8

2*(a + b) = 8*(a – b)

a + b = 4a – 4b

3a = 5b

a:b = 5:3

In what ratio should the profit of Rs.8000 be divided if X starts a business with an investment of Rs. 20000, Y invests Rs.7500 for 4 months and Z invests Rs.15000 after 3 months from the start of the business.

by
A. 16 : 2 : 3
B. 8 : 3 : 6
C. 16 : 2 : 9
D. 6 : 9 : 1
✅ The correct answer is option C. 16 : 2 : 9.
Let the profit of X be P1, that of Y be P2 and of Z be P3.

P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45

= 16 : 2 : 9