# Clock - Quantitative Aptitude

Q1. At what angle the hands of a clock are inclined at 15 minutes past 5 ?

(a) 67 ½°

(b) 69 ½°

(c) 73 ½°

(d) 77 ½°

**Answer:** (a) 67 ½°

Angle traced by hour hand in 5h15 min

= ( | 360 | X 5 + | 15 | )° |

12 | 60 |

= 157½°

Angle traced by min hand in 15 min = ((^{360}/_{12}) X 15)° = 90°

∴ Required angle = (157½)° - 90° = 67½°

Q2. A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 min 48 sec fast at 2 P.m. on the following Monday. When it was correct ?

(a) 6 PM Tuesday

(b) 12 PM Wednessday

(c) 2 PM Wednessday

(d) 4 PM Thursday

**Answer:** (c) 2 PM Wednessday

Time from 12 PM on Monday to 2 PM on the following Monday = 7 days 2 hours = 170 hours

The watch gains (2 + 4^{4}/_{5}) min = ^{34}/_{5} min

Now ^{34}/_{5} min are gained in 170 hrs

∴ 2 min are gained in (170 X (^{5}/_{34}) X 2) hrs = 50 hrs

So the watch is correct 2 days 2 hrs after 12 PM on Monday

i.e it will be correct at 2 PM on Wednessday

Q3. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together

(a) 5^{3}/_{11} min past 7

(b) 5^{5}/_{11} min past 7

(c) 5^{7}/_{11} min past 7

(d) 5^{11}/_{11} min past 7

**Answer:** (b) 5^{5}/_{11} min past 7

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart

At 7 o'clock they are 25 minute spaces apart

∴ Minute hand will have to gain only 5 minute spaces

55 minute, spaces are gained in 60 minute

5 minute spaces are gained in ((^{60}/_{55}) X 5) min = 5^{5}/_{11} min

∴ Required time = 5^{5}/_{11} min past 7

Q4. The reflex angle between the hands of a clock at 10.25 is

(a) 197 ½°

(b) 198 ½°

(c) 201 ½°

(d) 203 ½°

**Answer:** (a) 197 ½°

Angle traced by hour hand in ^{125}/_{12} hrs

= ( | 360 | X | 125 | )° |

12 | 2 |

= 312 ½°

Angle trace by minute hand in 25 minute = (^{360}/_{60}) X 25° = 150°

∴ Reflex angle = 360° - (312½ - 150°) = 197 ½°

**1**