Suppose, ‘A’ can complete a job in 10 days, and ‘A’ and ‘B’ together can complete the same job in 6 days. In how many days can ‘B’ alone complete the job ?<\/p>\n
[amp_mcq option1=”15 days” option2=”12 days” option3=”18 days” option4=”20 days” correct=”option1″]<\/p>\n
The combined work rate of A and B is the sum of their individual work rates:
\n(A’s rate) + (B’s rate) = (A+B)’s rate
\n(W \/ 10) + (W \/ x) = (W \/ 6)<\/p>\n
Since W represents the same job and is non-zero, we can divide the entire equation by W:
\n1 \/ 10 + 1 \/ x = 1 \/ 6<\/p>\n
Now, solve for 1\/x:
\n1 \/ x = 1 \/ 6 – 1 \/ 10<\/p>\n
To subtract the fractions, find a common denominator for 6 and 10. The least common multiple is 30.
\n1 \/ 6 = 5 \/ 30
\n1 \/ 10 = 3 \/ 30<\/p>\n
So, 1 \/ x = 5 \/ 30 – 3 \/ 30
\n1 \/ x = (5 – 3) \/ 30
\n1 \/ x = 2 \/ 30
\n1 \/ x = 1 \/ 15<\/p>\n