A, B and C can alone do a work in 15 days, 20 days and 30 days, respectively. They work together for some time after which C leaves. A total of Rs. 18000 is paid for the work and B gets Rs. 6000 more than C. For how many days did A work?

<p>Let A and B work for m days and C for n days to complete the work. Therefore, </p><p><math><mrow><mfrac><mrow><mi>m</mi></mrow><mrow><mn>1</mn><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mn>2</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>3</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math>&nbsp;. (1)</p><p>Out of the total of Rs. 18000, B gets Rs. 6000 more than C.</p><p>i.e., &nbsp;<math><mrow><mfrac><mrow><mi>m</mi></mrow><mrow><mn>2</mn><mn>0</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>3</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>6</mn><mn>0</mn><mn>0</mn><mn>0</mn></mrow><mrow><mn>1</mn><mn>8</mn><mn>0</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math>&nbsp;. (2)</p><p>On adding Eqs. (1) and (2), we get</p><p><math><mrow><mfrac><mrow><mi>m</mi></mrow><mrow><mn>1</mn><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mi>m</mi></mrow><mrow><mn>2</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>⇒</mo><mi>m</mi><mo>=</mo><mn>8</mn></mrow></math></p>

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