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# Lines and Angles | PRMO 2019 | Question 7

Try this beautiful problem from the PRMO, 2019 based on Lines and Angles.

## Lines and Angles - PRMO 2019

On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+$\frac{b}{c}$ where a b c are positive integers with $b\lt c$ and $\frac{b}{c}$ in the reduced form. find a+b+c.

• is 107
• is 51
• is 840
• cannot be determined from the given information

### Key Concepts

Lines

Algebra

Angles

PRMO, 2019, Question 7

Higher Algebra by Hall and Knight

## Try with Hints

First hint

Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min

Second Hint

x min after 12 is 6x -$\frac{x}{2}$=90 or 270 (in degrees) then x =16$\frac{4}{11}$ or 49$\frac{1}{11}$

Final Step

Difference 32$\frac{8}{11}$ then a+b+c=32+8+11=51.

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