
At what time between, four o’clock & five o’clock, are the hands \[2\]minutes space apart?
Answer
484.2k+ views
Hint: Clock concept: - The dial of the clock is circular in shape and was divided into \[60\]equal minute space.
\[60\]minute space traces an angle \[{360^0}\]
\[1\]minute space traces an angle \[{60^0}\].
Complete step by step solution:
Minute spaces: The face or dial of watch is a circle whose circumference is divided into \[60\]equal parts, called minute spaces.
Hour hand & Minute hand: A clock has two hands, the smaller one is called the hour hand or shorthand, while the larger one is called minute hand or long hand.
In \[60\]equal minutes, the minute hand gains \[55\]minutes on the hour on the hour hand.
When the two hands are at right angles, they are \[15\]minutes spaces apart.
Angle traced by hour hand in \[12\]hours \[ = {360^0}\].
Angle traced by minute hand in \[60\]min \[ = {360^0}\].
Therefore,
At 4 o’clock the two hands are 20-minute spaces apart.
To be in 2 minute, they must be 2 minute spaces apart.
Minute hand will have to gain \[\left( {20 + 2 = 22} \right)\]minute spaces.
As we know that,
\[55\]minute spaces are gained in \[60\]minute.
\[22\]minute spaces are gained in \[\dfrac{{60}}{{55}} \times 2\]minute\[ = 24\]minute.
Hence the hands will be \[2\]minute apart at \[24\]minute past.
Note: If the clock or watch indicates \[6\]hour \[10\]minute when the correct time is \[6\], it is said that the clock is \[10\]minute too fast.
If it indicates \[6:40\]when the correct time is \[7\], it is said to be \[20\]min slow.
\[60\]minute space traces an angle \[{360^0}\]
\[1\]minute space traces an angle \[{60^0}\].
Complete step by step solution:
Minute spaces: The face or dial of watch is a circle whose circumference is divided into \[60\]equal parts, called minute spaces.
Hour hand & Minute hand: A clock has two hands, the smaller one is called the hour hand or shorthand, while the larger one is called minute hand or long hand.
In \[60\]equal minutes, the minute hand gains \[55\]minutes on the hour on the hour hand.
When the two hands are at right angles, they are \[15\]minutes spaces apart.
Angle traced by hour hand in \[12\]hours \[ = {360^0}\].
Angle traced by minute hand in \[60\]min \[ = {360^0}\].
Therefore,

At 4 o’clock the two hands are 20-minute spaces apart.
To be in 2 minute, they must be 2 minute spaces apart.
Minute hand will have to gain \[\left( {20 + 2 = 22} \right)\]minute spaces.
As we know that,
\[55\]minute spaces are gained in \[60\]minute.
\[22\]minute spaces are gained in \[\dfrac{{60}}{{55}} \times 2\]minute\[ = 24\]minute.
Hence the hands will be \[2\]minute apart at \[24\]minute past.
Note: If the clock or watch indicates \[6\]hour \[10\]minute when the correct time is \[6\], it is said that the clock is \[10\]minute too fast.
If it indicates \[6:40\]when the correct time is \[7\], it is said to be \[20\]min slow.
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Master Class 9 English: Engaging Questions & Answers for Success

Master Class 9 Science: Engaging Questions & Answers for Success

Master Class 9 Social Science: Engaging Questions & Answers for Success

Master Class 9 Maths: Engaging Questions & Answers for Success

Class 9 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Difference Between Plant Cell and Animal Cell

What is pollution? How many types of pollution? Define it

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.
