A train covers three equal distances at speeds in the ratio 4 : 5 : 6. What is the ratio of its average speed to its minimum speed over the entire journey?
A train covers three equal distances at speeds in the ratio 4 : 5 : 6. What is the ratio of its average speed to its minimum speed over the entire journey?
एक ट्रेन तीन समान दूरियाँ क्रमशः 4 : 5 : 6 के अनुपात वाली गतियों से तय करती है। पूरी यात्रा के दौरान उसकी औसत गति और न्युनतम गति का अनुपात क्या है?
Detailed Solution & Logic
Correct Answer:
45 : 37
$4x,\ 5x,\ 6x$
$\text{Average speed}=\dfrac{3}{\dfrac{1}{4x}+\dfrac{1}{5x}+\dfrac{1}{6x}}=\dfrac{3}{\dfrac{15+12+10}{60x}}=\dfrac{180x}{37}$
$\text{Minimum speed}=4x$
$\text{Required ratio}=\dfrac{180x}{37}:4x=180:148=45:37$
$\boxed{45:37}$
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