A) 3, 8
B) 8, 3
C) 10, 5
D) 5, 10
Correct Answer: A
Solution :
(a): Since, it is also given that, in 13 hours the boat can go 40 km upstream and 55 km downstream. We get the equation. \[\frac{40}{x-y}+\frac{55}{x+y}=13\]??????(2) Put \[\frac{1}{x-y}=u\] and \[\frac{1}{x+y}=v\]?????.(3) On substituting these values in Equations (1) (as illustrated in solution to question 38) and (2), we get the pair of linear equations: \[33u+44v=10\] or \[30u+44v-10=0\]???(4) \[40u+55v=13\text{ }\]or \[40u+55v-13=0\]???(5) Using Cross ? multiplication method, we get \[\frac{u}{44(-13)-55(-10)}=\frac{v}{40(-10)-30(-13)}\] \[=\frac{1}{30(55)-44(40)}\] i.e., \[\frac{u}{-22}=\frac{v}{-10}=\frac{1}{-110}\] i.e., \[u=\frac{1}{5},v=\frac{1}{11}\] Now put these values of u and v in equations (3), we get \[\frac{1}{x-y}=\frac{1}{5}\] and \[\frac{1}{x+y}=\frac{1}{11}\] i.e. \[x-y=5\]and \[x+y=11\]????.(6) Adding these equations, we get, \[2x=16\]i.e., \[x=8\] Subtracting the equations in (6), we get \[2y=6\] i.e., \[y=3\] Hence, the speed of the boat in still water is 8 km/h and the speed of the stream is 3 km/h
You need to login to perform this action.
You will be redirected in
3 sec
