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प्रश्न
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?
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उत्तर
\[\text{ Time taken by } \left( A + B \right) \text{ to do the work = 12 days } \]
\[\text{ Time taken by } \left( B + C \right) \text{ to do the work = 15 days } \]
\[ \text{ Time taken by } \left( A + C \right) \text{ to do the work = 20 days } \]
\[ \text{ Now, } \]
\[\text{ Work done by } \left( A + B \right) = \frac{1}{12}\]
\[ \text{ Work done by } \left( B + C \right) = \frac{1}{15}\]
\[ \text{ Work done by } \left( A + C \right) = \frac{1}{20}\]
\[ \therefore \text{ Work done together } = \left( A + B \right) + \left( B + C \right) + \left( A + C \right)\]
\[ = \frac{1}{12} + \frac{1}{15} + \frac{1}{20}\]
\[ = \frac{5 + 4 + 3}{60} = \frac{12}{60}\]
\[ = \frac{1}{5}\]
\[ \therefore \text{ Work done together } = 2\left( A + B + C \right) = \frac{1}{5}\]
\[ \therefore \text{ Work done by } \left( A + B + C \right) = \frac{1}{10}\]
\[ \therefore \text{ Work done by A alone } = \left( A + B + C \right) - \left( B + C \right)\]
\[ = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30}\]
\[\text{ Thus, A alone can do the work in 30 days } .\]
संबंधित प्रश्न
In which of the following tables x and y vary directly?
(i)
| a | 7 | 9 | 13 | 21 | 25 |
| b | 21 | 27 | 39 | 63 | 75 |
(ii)
| a | 10 | 20 | 30 | 40 | 46 |
| b | 5 | 10 | 15 | 20 | 23 |
(iii)
| a | 2 | 3 | 4 | 5 | 6 |
| b | 6 | 9 | 12 | 17 | 20 |
(iv)
| a | 12 | 22 | 32 | 42 | 52 |
| b | 13 | 23 | 33 | 43 | 53 |
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