Problem: A takes m times as long to do a piece of work as B and C together; B takes n times as long as C and A together; and C takes x times as long as A and B together. Then x, in terms of m and n, is:
Answer Choices:
A. m+n2mn​
B. 2(m+n)1​
C. m+n−mn1​
D. m+n+2mn1−mn​
E. mn−1m+n+2​
Solution:
A1​= m1​( B1​+C1​), B1​=n1​(C1​+ A1​),C1​=x1​( A1​+ B1​)
∴Am​−Bn​=B1​−A1​ and Am​+Bn​=B1​+A1​+C2​=B1​+A1​+x2​(A1​+B1​)
∴A1​(m+1)=B1​(n+1) and A1​(m−1−x2​)=B1​(1−n+x2​)
∴BA​=n+1m+1​ and BA​=1−n+2/xm−1−2/x​∴n+1m+1​=1−n+2/xm−1−2/x​∴x=mn−1m+n+2​