Advertisements
Advertisements
प्रश्न
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Advertisements
उत्तर
Let the speed of the stream be x km/hr.
∴ Speed of the boat downstream = (15 + x) km/hr
Speed of the boat upstream = (15 – x) km/hr
Time taken to go 30 km downstream = `30/(15 + x)` hr
Time taken to come back = `30/(15 - x)` hr
From the given information,
`30/(15 + x) + 30/(15 - x) = 4 30/60`
`30/(15 + x) + 30/(15 - x) = 9/2`
`(450 - 30x + 450 + 30x)/((15 + x)(15 - x)) = 9/2`
`900/(225 - x^2) = 9/2`
`100/(225 - x^2) = 1/2`
225 – x2 = 200
x2 = 25
x = ±5
But, x cannot be negative, so, x = 5.
Thus, the speed of the stream is 5 km/hr.
संबंधित प्रश्न
A stone is thrown vertically downwards and the formula d = 16t2 + 4t gives the distance, d metres, that it falls in t seconds. How long does it take to fall 420 metres?
One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Find their present ages.
Mr. Mehra sends his servant to the market to buy oranges worth Rs. 15. The servant having eaten three oranges on the way, Mr. Mehra pays Rs. 25 paise per orange more than the market price. Taking x to be the number of oranges which Mr. Mehra receives, form a quadratic equation in x. Hence, find the value of x.
Rs. 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paise less. Find the number of children.
A trader bought a number of articles for Rs. 1,200. Ten were damaged and he sold each of the remaining articles at Rs. 2 more than what he paid for it, thus getting a profit of Rs. 60 on the whole transaction. Taking the number of articles he bought as x, form an equation in x and solve it.
A hotel bill for a number of people for overnight stay is Rs. 4800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs. 200. Find the number of people staying overnight.
Rs. 6500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs. 30 less. Find the original number of persons.
The ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more, then each would have got Rs. 12 less. Find ‘x’.
₹ 320 were divided equally among 8 children. If 2 more children join them, each will get, how many rupees more or less?
