Question Number 100908 by bemath last updated on 29/Jun/20

what the value of angle  formed by a long needle and   short needle on analog clock   that shows at 15.50 ?  (A) 175^o    (B) 174^o    (C) 173^o   (D) 172^o     (E) 170^o

Commented last updated on 29/Jun/20

θ=∣((11)/2).m−30.h∣       [m=minute,h=houre]  𝛉=∣((11)/2)×50−30×15∣=∣−175∣=175^• ■

Commented bybemath last updated on 29/Jun/20

yes sir correct answer 175^o

Answered by 1549442205 last updated on 29/Jun/20

At 15 o′clock the long needle′end  and short  needle′s end are spaced  a quarter distance  of circle away from each other.  The speed of the long needle′s end  equal (1/(60))(circle per a minute) and of   short needle equal (1/(12×60))(circle per a minute)  Hence after 50 minutes the long needle′s end  went a distance equal (1/(60))×50=(5/6)(circle)  while the short needle′s end went a distance  equal 50×(1/(720))=(5/(72))(circle).Therefore,  at 15.50 the arc create by ends of both  the needles has the length equal   (5/6)−((1/4)+(5/(72)))=((37)/(72))(circle)which means  that it create an angle has the value  equal ((37)/(72))×360°=185°  Please,sir check to help me is it correct?

Commented bybemath last updated on 29/Jun/20

means there is no correct answer  option?

Commented byEuclidKaBaap last updated on 29/Jun/20

hahahaha..   its simple thing we  often oversee .. its a reflex angle and  they havent specified which side..  so 360−185=175 will be the required  answer asked in the question

Commented by1549442205 last updated on 29/Jun/20

Thank you sir,a simple thing that I  don′t think out !The angle is created by  long hand and the short hand (clockwise)  equal 360°−185°=175°,so choose answer  A:175°

Answered by ajfour last updated on 29/Jun/20

At   15:00   angle is 90°.  360° of minute hand ≡ 30° hour hand  300° of minute hand≡ (((300)/(12)))^° hour hand  shorter angle between them at  15:50   is       = 60°+90°+(((300)/(12)))^°        = 175° .