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.
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.
APPEARS IN
संबंधित प्रश्न
The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.
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.
The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of the son. Find their present ages.
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.
The total cost price of a certain number of identical articles is Rs. 4800. By selling the articles at Rs. 100 each, a profit equal to the cost price of 15 articles is made. Find the number of articles bought.
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.
Mohan takes 16 days less than Manoj to do a piece of work. If both working together can do it in 15 days, in how many days will Mohan alone complete the work?
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by `1/14`. Find the fraction.
The ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.
