Advertisements
Advertisements
प्रश्न
Two pipes running together can fill a tank in `11 1/9` minutes. If on pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank
separately.
उत्तर
Let the time taken by one pipe to fill the tank be x minutes.
∴Time taken by the other pipe to fill the tank = (x +5)min
Suppose the volume of the tank be V.
Volume of the tank filled by one pipe in x minutes = V
∴Volume of the tank filled by one pipe in 1 minute =`V/x`
⇒ Volume of the tank filled by one pipe in `11 1/9` minutes = `V/x xx11 1/9=V/x xx100/9`
Similarly,
Volume of the tank filled by the other pipe in `11 1/9` minutes= `V/(x+5)xx11 1/9=V/(x+5)xx100/9`
Now,
Volume of the tank filled by one pipe in `11 1/9` minutes + Volume of the tank filled by the other pipe in `11 1/9`=V
∴`V (1/x+1/(x+5))xx100=V`
⇒` 1/x+1/(x+5)=9/100`
⇒ `(x+5+x)/(x(x+5))=9/100`
⇒`(2x+5)/(x^2+5x)=9/100`
⇒`200x+500=9x^2+45x`
⇒`9x^2-155x-500=0`
⇒`9x^2-180x+25x-500=0`
⇒ `9x(x-20)+25(x-20)=0`
⇒`(x-20) (9x+25)=0`
⇒`x-20=0 or 9x+25=0`
⇒` x=20 or x=-25/9`
∴ `x=20` (Time cannot be negative)
Time taken by one pipe to fill the tank = 20 min
Time taken by other pipe to fill the tank = (20+5) 25 min
APPEARS IN
संबंधित प्रश्न
Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.
Three consecutive positive integers are such that the sum of the square of the first and product of the other two is 46. Find the integers.
Some students planned a picnic. The total budget for food was ₹ 2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by ₹ 20. How many students attended the picnic and how much did each student pay for the food?
A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.
While boarding an aeroplane, a passengers got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30
minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane.
Do you appreciate the values shown by the pilot, namely promptness in providing help to
the injured and his efforts to reach in time?
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.
A motor boat whose speed in still water is 178 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream
The length of a rectangular field is three times its breadth. If the area of the field be 147 sq meters, find the length of the field.
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
The speed of a motorboat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more upstream than downstream.
Let the speed of the stream be x km/hr then the speed of the motorboat upstream will be:
