Advertisements
Advertisements
Question
A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?
Advertisements
Solution
\[\text{ Time taken by } \left( A + B \right) \text{ to do the work = 12 days } \]
\[\text{ Time taken by } \left( B + C \right) \text{ to do the work = 15 days } \]
\[ \text{ Time taken by } \left( A + C \right) \text{ to do the work = 20 days } \]
\[ \text{ Now, } \]
\[\text{ Work done by } \left( A + B \right) = \frac{1}{12}\]
\[ \text{ Work done by } \left( B + C \right) = \frac{1}{15}\]
\[ \text{ Work done by } \left( A + C \right) = \frac{1}{20}\]
\[ \therefore \text{ Work done together } = \left( A + B \right) + \left( B + C \right) + \left( A + C \right)\]
\[ = \frac{1}{12} + \frac{1}{15} + \frac{1}{20}\]
\[ = \frac{5 + 4 + 3}{60} = \frac{12}{60}\]
\[ = \frac{1}{5}\]
\[ \therefore \text{ Work done together } = 2\left( A + B + C \right) = \frac{1}{5}\]
\[ \therefore \text{ Work done by } \left( A + B + C \right) = \frac{1}{10}\]
\[ \therefore \text{ Work done by A alone } = \left( A + B + C \right) - \left( B + C \right)\]
\[ = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30}\]
\[\text{ Thus, A alone can do the work in 30 days } .\]
RELATED QUESTIONS
In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
For 9 cows, 13 kg 500 g of food supplements are required every day. In the same proportion, how much will be needed for 12 cows?
If 45 persons can complete a work in 20 days, then the time taken by 75 persons will be ______ hours.
Write whether the following statement vary directly, vary inversely with each other, or neither of the two.
The distance travelled by CNG bus and the amount of CNG used.
Write whether the following statement vary directly, vary inversely with each other, or neither of the two.
Number of students in a hostel and consumption of food.
Write whether the following statement vary directly, vary inversely with each other, or neither of the two.
Area of land and its cost.
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 A | Mixture B |
 |
 |
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?
Kusum always forgets how to convert miles to kilometres and back again. However she remembers that her car’s speedometer shows both miles and kilometres. She knows that travelling 50 miles per hour is same as travelling 80 kilometres per hour. To cover a distance of 200 km, how many miles Kusum would have to go?
