Question
At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
Answer: Option D
At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
∴ Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min.
50 min. spaces are gained in
$$\eqalign{
& \left( {\frac{{60}}{{55}} \times 50} \right){\text{min}}{\text{.}}\,{\text{or}}\,54\frac{6}{{11}}\,{\text{min}}. \cr
& \therefore {\text{Required}}\,{\text{time}} \cr
& = 54\frac{6}{{11}}{\text{min}}{\text{.}}\,{\text{past}}\,4 \cr} $$
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At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
∴ Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min.
50 min. spaces are gained in
$$\eqalign{
& \left( {\frac{{60}}{{55}} \times 50} \right){\text{min}}{\text{.}}\,{\text{or}}\,54\frac{6}{{11}}\,{\text{min}}. \cr
& \therefore {\text{Required}}\,{\text{time}} \cr
& = 54\frac{6}{{11}}{\text{min}}{\text{.}}\,{\text{past}}\,4 \cr} $$
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