Advertisements
Advertisements
प्रश्न
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
Advertisements
उत्तर
Speed of a boat in still water = 11 km/hr
Let the speed of stream = x km/hr.
Distance covered = 12 km.
Time taken = 2 hours 45 minutes
= `2(3)/(4) = (11)/(4)`hours
Now according to the condition
`(12)/(11 - x) + (12)/(11 + x) = (11)/(4)`
⇒ `(12(11 + x + 11 - x))/((11 - x)(11 + x)) = (11)/(4)`
⇒ `(12 xx 22)/(121 - x^2) = (11)/(4)`
⇒ 1331 – 11x2 = 4 x 12 x 22 = 1056
⇒ 1331 – 11x2 = 1056
⇒ 1331 – 1056 – 11x2 = 0
⇒ -11x2 + 275 = 0
⇒ x2 – 25 = 0 ...(Dividing by -11)
⇒ (x + 5)(x – 5) = 0
Either x + 5 = 0,
then x = –5,
but it is not possible as it is in negative.
or
x – 5 = 0,
then x = 5
Hence speed of stream = 5km/hr.
APPEARS IN
संबंधित प्रश्न
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
Solve the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Solve the following equation by factorization
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
If the product of two consecutive even integers is 224, find the integers.
The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm2, find x.
