Question

a Boat covers 27 kilometre in upstream in same time as it covers 36 km downstream speed of stream is what percent of the speed of boat in upstream​

Answer 1

Answer:

$\red { Required \: percentage}\green {= 16.67 \%}$

Step-by-step explanation:

$Let \: speed \: of \: the \: boat \: in \: still\\water = x \: km/h$

$Speed \: of \: the \: stream = y \: km/h$

$Speed \: of \:the \: in \: down \:stream \\= (x+y) \: km/h$

$Distance \: travelled = 36 \:km$

$Time = \frac{ Distance }{speed }\\= \frac{36}{x+y} \: ---(1)$

$Speed \: of \:the \: in \: Up \:stream \\= (x-y) \: km/h$

$Distance \: travelled = 27 \:km$

$Time = \frac{ Distance }{speed }\\= \frac{27}{x-y} \: ---(2)$

/* According to the problem given,

$(1) = (2)$

$\implies \frac{ 36}{x+y} = \frac{27}{x-y}$

$\implies \frac{x-y}{x+y} = \frac{27}{36}\\= \frac{3}{4}$

$Let \: x - y = 3k \: ---(3)\\and \: x+y = 4k \:---(4)$

$Add \: equations \: (3) \: and \: ( 4) , we \:get$

$2x = 7k$

$\implies x = \frac{7k}{2}$

/* Put x value in equation (4), we get

$\implies \frac{7k}{2} + y = 4k$

$\implies y = 4k - \frac{7k}{2}$

$\implies y = \frac{ 8k -7k}{2}$

$\implies y = \frac{k}{2}\: ---(5)$

$Required \: percentage = \frac{y}{x-y} \\= \frac{ \frac{k}{2}}{\frac{3k}{1}}\\= \frac{ k}{2} \times \frac{1}{3k} \\= \frac{1}{6}$

$≈ 16.67 \%$

Therefore.,

$\red { Required \: percentage}\green {= 16.67 \% }$

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