Question

A watch which gains 5 seconds in 3 minutes was set right at 9 am. In the evening of the same day, when the watch
indicated quarter past 6 o'clock, the true time is:
6 pm
7
59 min past 5
12
7
57 min past 5
12
5
min past 5
2.
2​

Answer 1

Given :

• A watch which gains 5 seconds in 3 minutes was set right at 9 am. In the evening of the same day, when the watch indicated quarter past 6 o'clock

To find :

• true time

Solution :

Time from 9 a.m. to 6.15 p.m. = 9 hrs 15 min.

37/4 hrs. 3 min. 5 sec. of this clock = 3 min. of the correct clock.

= 37/720 hrs of this clock

= 1/20 hrs of the correct clock

= 37/4 hrs of this clock

= 1/20 x 720/37 x 37/4 hrs of the correct clock

= 9 hrs of the correct clock

∴ The correct time is 9 hrs after 9 a.m. i.e.6 p.m.

Answer 2

$\huge\bf{\underbrace{\gray{GIVEN:-}}}$

• A watch which gains 5 seconds in 3 minutes was set right at 9 a.m .

$\huge\bf{\underbrace{\gray{TO\:FIND:-}}}$

• The true time, when the watch indicated quarter past 6 o'clock .

$\huge\bf{\underbrace{\gray{SOLUTION:-}}}$

☯︎ Time from 9 a.m. to quarter past 6 o' clock is,

➪ 9 hours 15 minutes

➪ (9 × 60) minutes + 15 minutes

➪ (540 + 15) minutes

➪ $\bf\red{555\:min.}$ or $\bf\red{\dfrac{37}{4}\:hrs.}$

☯︎ 3 min. 5 sec. of this clock = 3 min. of the correct clock .

⇒ $\bf{\dfrac{37}{720}\:hrs.}$ of this clock = $\bf{\dfrac{1}{20}\:hrs.}$ of the correct clock .

⇒ 1 hrs. of this clock = $\bf{\Big(\dfrac{1}{20}\times{\dfrac{720}{37}}\Big)\:hrs.}$ of the correct clock .

⇒$\bf{\dfrac{37}{4}\:hrs.}$ of this clock = $\bf{\Big(\dfrac{1}{20}\times{\dfrac{720}{37}}\times{\dfrac{37}{4}}\Big)\:hrs.}$ of the correct clock .

⇒ $\bf{\dfrac{37}{4}\:hrs.}$ of this clock = 9 hrs. of the correct clock .

$\huge\red\therefore$ The correct time is 9 hrs. after 9 a.m, i.e. 6 p.m. .