To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. - Mathematics

Advertisements
Advertisements

To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.

Advertisements

Solution

Let the time taken by the pipe of larger diameter to fill the pool completely be x hours and the pipe of smaller diameter be y hours.

In one hour,

Part of the pool filled by the pipe of larger diameter = `1/x`

Part of the pool filled by the pipe of smaller diameter = `1/y`

According to question,

`4/x+9/y=1/2`

yx=10             .....(ii)

Substituting the value of y from (ii) in (i), we get

`4/x+9/(x+10)=1/2`

`(4(x+10)+9x)/((x+10)x)=1/2`

`(4x+40+9x)/(x^2+10x)=1/2`

`(13x+40)/(x^2+10x)=1/2`

26x+80=x2+10x

x216x80=0

x220x+4x80=0

x(x20)+4(x20)=0

(x+4)(x20)=0

x=20

Putting the value of x in (ii), we get

y20=10

y=30

Therefore, the time taken by the pipe of larger diameter to fill the pool is 20 hours and the time taken by the pipe of smaller diameter to fill the pool is 30 hours

  Is there an error in this question or solution?
2014-2015 (March) Delhi Set 2

RELATED QUESTIONS

Find the volume of a sphere of diameter 6 cm.


Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.


Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm, 90 cm, and 30 cm respectively. How many balls were melted to make the tube?


A metal parallelopiped of measures 16 cm x 11 cm x 10 cm was melted to make coins. How many coins were made if the thickness and diameter of each coin were 2 mm and 2 cm respectively?


The diameter and length of a roller is 120 cm and 84 cm respectively. To level the ground, 200 rotations of the roller are required. Find the expenditure to level the ground at the rate of Rs. 10 per sq.m.


Find the ratio of the volumes of a cylinder and a cone having equal radius and equal height.
(A)1 : 2 (B) 2 : 1 (C) 1 : 3 (D) 3 : 1


Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.


The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.


A cylindrical vessel 32 cm high and 18 cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, the radius of its base is


A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.


A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total
surface area of the toy.


Choose the correct answer of the following question:

A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is


A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of canvas required is


Assertion (A)
If the radii of the circular ends of a bucket 24 cm high are 15 cm and 5 cm, respectively, then the surface area of the bucket is 545π cm2.

  1. Reason(R)
    If the radii of the circular ends of the frustum of a cone are R and r, respectively, and its height is h, then its surface area is 
  2. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  3. Assertion (A) is true and Reason (R) is false.
  4. Assertion (A) is false and Reason (R) is true.

In a right circular cone, if the perpendicular height is 12 cm and the radius is 5 cm, then find its slant height.


Find the surface area of a sphere of radius 3.5 cm.


How many solid cylinders of radius 6 cm and height 12 cm can be made by melting a solid sphere of radius 18 cm? 

Activity: Radius of the sphere, r = 18 cm

For cylinder, radius R = 6 cm, height H = 12 cm 

∴ Number of cylinders can be made =`"Volume of the sphere"/square`

`= (4/3 pir^3)/square`

`= (4/3 xx 18 xx 18 xx 18)/square`

= `square`


The dimensions of a metallic cuboid are 44 cm × 42 cm × 21 cm. it is molten and recast into a sphere. Find the surface area of the sphere.


If the side of a cube is 5 cm, then find its volume. 


Tick the object which has more volume


Arrange the given objects according to their volume


Arrange the given objects according to their volume


Arrange the given objects according to their volume


A metal cuboid of measures 16 cm × 11 cm × 10 cm was melted to make coins. How many coins were made, if the thickness and diameter of each coin was 2 mm and 2 cm respectively? (π = 3.14)


What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w units?


The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 square centimetres. The volume of the solid, in cubic centimetres, is ______.


If R is the radius of the base of the hat, then the total outer surface area of the hat is ______.


______ of a solid is the measurement of the space occupied by it.


______ surface area of room = area of 4 walls.


Ratio of area of a circle to the area of a square whose side equals radius of circle is 1 : π.


The circumference of the front wheel of a cart is 3 m long and that of the back wheel is 4 m long. What is the distance travelled by the cart, when the front wheel makes five more revolutions than the rear wheel?


Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. Find the area left ungrazed by the horses.


A running track has 2 semicircular ends of radius 63 m and two straight lengths. The perimeter of the track is 1000 m. Find each straight length.


The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. How many square metres of metal sheet would be needed to make it?


The internal and external radii of a spherical shell are 3cm and 5cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder. Also find the total surface area of the cylinder. (Take `pi = 22/7`)


A tent is a shape of a triangular 'prism' resting on a rectangular side PQ = PR, PT = 1.5 m, QR = 1.8 m, length of the tent = 3 m. Find:

  1. ∠PQR
  2. The volume of the tent


If the length of the diagonal of a cube is `5sqrt(3)` cm, find the total surface area.

Length of the diagonal of the cube = `square`

So, `square` = `5sqrt(3)`

⇒ Side = `square`

Total surface area of cube = `square`

= `square` × `square` × `square`

= `square` cm2

 Hence, the total surface area is `square`.


The radius of a metallic sphere is 8 cm. It was melted to make a wire of diameter 6 mm. Find the length of the wire.


The surface area of a sphere is 616 sq cm. Find its radius tan β = `3/4`


Share
Notifications



      Forgot password?
Use app×