Question Number 46996 by Raj Singh last updated on 03/Nov/18
Answered by tanmay.chaudhury50@gmail.com last updated on 03/Nov/18
$${A}\:{perform}\:\frac{\mathrm{1}}{\mathrm{15}}\:{portion}\:{of}\:{work}\:{in}\:\mathrm{1}\:{day} \\ $$$${B}\:{perform}\:\frac{\mathrm{1}}{\mathrm{20}}{portion}\:{of}\:{work}\:{in}\:\mathrm{1}\:{day} \\ $$$${both}\:{perform}\:\left(\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{20}}=\frac{\mathrm{4}+\mathrm{3}}{\mathrm{60}}=\frac{\mathrm{7}}{\mathrm{60}}{portion}\:{in}\:\mathrm{1}\:{day}\right. \\ $$$${both}\:{perform}\:\mathrm{6}×\frac{\mathrm{7}}{\mathrm{60}}=\frac{\mathrm{7}}{\mathrm{10}}{portion}\:{in}\:\mathrm{6}\:{day} \\ $$$${remaining}\:{work}=\mathrm{1}−\frac{\mathrm{7}}{\mathrm{10}}=\frac{\mathrm{3}}{\mathrm{10}}{portion} \\ $$$${A}\:{perform}\:\frac{\mathrm{1}}{\mathrm{15}}{portion}\:{in}\:\mathrm{1}\:{day} \\ $$$${A}\:{perform}\:\mathrm{1}\:{portion}\:{in}\:\mathrm{15}\:{days} \\ $$$${so}\:{A}\:{perform}\:\frac{\mathrm{3}}{\mathrm{10}\:}\:{portion}\:{in}\:\frac{\mathrm{3}}{\mathrm{10}}×\mathrm{15}=\frac{\mathrm{9}}{\mathrm{2}}=\mathrm{4}.\mathrm{5}\:{days} \\ $$$$ \\ $$