Question
Quantity I:Â Boat 'P' travels
540 m downstream in 45 seconds, while boat 'Q' travels 240 m upstream in 48 seconds. If the ratio of the speed of boat P in still water to the speed of boat Q in still water is 19:15, find the time it takes for boat 'P' to cover 224 m upstream. Quantity II:Â In a mixture of juice and water, the amount of juice exceeds the amount of water by 6 liters. The ratio of the cost of pure juice to the cost of the mixture is 5:3. If 5 liters of the mixture is replaced with the same quantity of juice, what will be the new cost of the mixture? In the question, two quantities I and II are given. You have to solve both the quantities to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.Solution
ATQ, Quantity I: Let the speeds of boats P and Q in still water are ‘19x’ m/s and ‘15x’ m/s respectively. Also let the speed of the stream is ‘y’ m/s. So, 19x+y= 540/45 19x + y = 12 ---------- (1) And 15x-y= 240/48 15x – y = 5 ---------- (2) From equations (1) and (2): x = 0.5, y = 2.5 Since, the upstream speed of boat P = 19 × 0.5 – 2.5 = 7 m/s So, the time, in which boat P can cover 224 m upstream = 224/7 = 32 seconds Quantity II: Let the initial quantity of water = ‘x’ L So, the initial quantity of juice = (x + 6) L Let the cost of pure juice is Rs.’5y’ per L and the initial cost of the mixture is Rs.‘3y’ per L. So, ((x+6)×5y)/(2x+6)=3y 5x + 30 = 6x + 18 x = 12 The initial quantity of water = 12 L The initial quantity of water = 12 L The initial quantity of juice = 12 + 6 = 18 L After replacing 5 L quantity of the mixture with the same quantity of juice: The new quantity of juice = 18 – 3 + 5 = 20 L The new quantity of water = 12 – 2 = 10 L Since, we don’t know the cost of the pure juice. So, the cost of new mixture can’t be determined. Hence, relation can’t be established
A and B together can finish a work in 10 days. If A alone can finish it in 25 days, in how many days can B alone finish it?
A man, a woman and a boy can do a work in 4, 8, 16 days respectively. How many boys were required with 1 man and 1 woman to complete the same work in 1/...
A man is thrice as fast as a women and a woman is twice as fast as a boy. If all of them can do a work in 18 days. than a boy can do the work in?
x men can finish a work in y days. 0.9x women can finish 1/3rd of the same work in (y - 8) days. If 0.8x women can complete 1/3rd work in 36 days. Find ...
'Ramesh' can complete a work in 40 days. He started the work and left after 24 days from starting. The remaining work was done by 'Suresh' in 30 days. F...
A and B finish a job together in 36 days, while B and C together finish it in 48 days. The trio completes 75% of the job in 18 days. In how many days wi...
There is enough food in a camp to last for 50 days if each of the 40 soldiers present at the camp eat 2 times a day. After 20 days, 40 more soldiers jo...
- Suppose D, E and F can do a piece of work individually in 18, 27 and 36 days respectively. If they combine and work for 4 days, what percentage of work wou...
- A builder employed 12 workers to complete a job in 18 days. But after 8 days, 4 workers quit. How many more days will be required to complete the remaining...
Twenty laborers can complete a piece of work in 12 days. If 20 laborers started working and after 3 more days, additional laborers joined to complete th...
Relevant for Exams:
