Advertisements
Advertisements
Question
A cistern can be filled by one tap in 8 hours, and by another in 4 hours. How long will it take to fill the cistern if both taps are opened together?
Advertisements
Solution
\[\text{ Time taken by the first tap to fill the cistern = 8 hours } \]
\[\text{ Time taken by the second tap to fill the cistern = 4 hours } \]
\[ \therefore \text{ Work done by the first tap in 1 hour } = \frac{1}{8}\]
\[ \text{ Work done by the second tap in 1 hour } = \frac{1}{4}\]
\[ \therefore \text{ Work done by both the taps in 1 hour } = \frac{1}{8} + \frac{1}{4}\]
\[ = \frac{1 + 2}{8} = \frac{3}{8}\]
\[\text{ Thus, both the taps together will fill the cistern in } \frac{8}{3} \text{ hours or } 2\frac{2}{3} \text{ hours } .\]
APPEARS IN
RELATED QUESTIONS
Rakesh can do a piece of work in 20 days. How much work can he do in 4 days?
A, B and C can reap a field in \[15\frac{3}{4}\] days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?
A truck requires 108 liters of diesel for covering a distance of 594 km. How much diesel will be required to cover a distance of 1650 km?
Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?
Write whether the following statement vary directly, vary inversely with each other, or neither of the two.
Area of the walls of a room and the cost of white washing the walls.
Campus and Welfare Committee of school is planning to develop a blue shade for painting the entire school building. For this purpose various shades are tried by mixing containers of blue paint and white paint. In the following mixtures, decide which is a lighter shade of blue and also find the lightest blue shade among all of them.
| Mixture G | Mixture H |
 |
 |
If one container has one litre paint and the building requires 105 litres for painting, how many container of each type is required to paint the building by darkest blue shade?
Ravi starts for his school at 8:20 a.m. on his bicycle. If he travels at a speed of 10 km/h, then he reaches his school late by 8 minutes but on travelling at 16 km/h he reaches the school 10 minutes early. At what time does the school start?
A water tank casts a shadow 21 m long. A tree of height 9.5 m casts a shadow 8 m long at the same time. The lengths of the shadows are directly proportional to their heights. Find the height of the tank.
A volleyball court is in a rectangular shape and its dimensions are directly proportional to the dimensions of the swimming pool given below. Find the width of the pool.
The students of Anju’s class sold posters to raise money. Anju wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. Could Anju’s class raise exactly Rs 2,000? If so, how many posters would they need to sell? If not, why?
