At what time between 5.30 and 6 will the hands of a clock be at right angles?

143 ⁵/₁₁ min. past 5
243 ⁷/₁₁ min. past 5
340 min. past 5
445 min. past 5

Answer:- 1

Explanation:-

Solution:

At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in

\begin{aligned} (\frac{60}{55} \times 40) min = 43 \frac{7}{11} min \\ ∴ Required time = 43 \frac{7}{11} min . p a s t 5 \end{aligned}

$\eqalign{ & \left( {\frac{{60}}{{55}} \times 40} \right)\,\min = 43\frac{7}{{11}}\,\min \cr & \therefore {\text{Required}}\,{\text{time}} = 43\frac{7}{{11}}\,\min .\,past\,5 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} (\frac{60}{55} \times 40) min = 43 \frac{7}{11} min \\ ∴ Required time = 43 \frac{7}{11} min . p a s t 5 \end{aligned}

$\eqalign{ & \left( {\frac{{60}}{{55}} \times 40} \right)\,\min = 43\frac{7}{{11}}\,\min \cr & \therefore {\text{Required}}\,{\text{time}} = 43\frac{7}{{11}}\,\min .\,past\,5 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }