Lesson Posted on 30 Apr CBSE/Class 7/Maths/Comparing quantity/Ratio and Proportion

Conversion of Ratio to Proportion & percentage.

Prasanna Reddy

I can teach every topic very easily and make it stronger for the students.

Comparing two quantities of same units( length, volume or currency etc.) is called 'ratio'. Example: A has 3 pens & B has 4 pens, then Ratio of the number of pens is 3:4 ( : pronounced as is to) or 3/4. we cannot compare 6 boys and 8 cows since cow & boy are not the same kinds, hence it is not... read more

Comparing two quantities of *sam*e *units(* length, volume or currency etc.) is called '*ra*tio'. Example: A has 3 pens & B has 4 pens, then Ratio of the number of pens is 3:4 ( : pronounced as *is to*) or 3/4.

we cannot compare 6 boys and 8 cows since cow & boy are not the same kinds, hence it is not the ratio. IF *two ratios* are *equal*, it is *proportion. ( 2/4=1/2).*

*A ratio is also called as a fraction (3/4). A f*raction with denominator 100 is called *percen*t. *per means by, cent = 100.*

*A *fraction when multiplied by 100 becomes *percen*tage ,symbol as %( i,e 1/2 x 100 = 50%) ex: 20% = 20/100)

Conversion of percentage into Ratio is as follows:

- 25 %( percentage) = 25/100 = 1/4(fraction) = 1:4 (ratio)

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Comments Asked on 24 Apr CBSE/Class 10/Mathematics CBSE/Class 5 CBSE/Class 6/Maths

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Lesson Posted on 03 Apr CBSE/Class 7/Maths

G Suresh

17 years of industrial experience Working in an automobile MNC

Average speed = Total distance / Total Time Eg. A car travels at a speed of 40 kmph for the onward journey and 50 kmph for the return journey. What is the average speed ? Ans) Let x be the distance travelled by the car for the onward and return journey each. So total distance is 2x kms. Time... read more

Average speed = Total distance / Total Time

Eg. A car travels at a speed of 40 kmph for the onward journey and 50 kmph for the return journey. What is the average speed ?

Ans) Let x be the distance travelled by the car for the onward and return journey each. So total distance is 2x kms.

Time = Distance / Speed

So time for the onward journey = x/40 hrs while time for the return journey = x/50 hrs

Total time = x/40 + x/50 = 9x/200 hrs

So Average speed = 2x / (9x/200) = 2/9 * 200 = 44.44 kmph

**Remember, for such kind of problems do not simply take the average of onward and return journeys.**

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Comments Lesson Posted on 03 Apr CBSE/Class 7/Maths

Time and Distance: Upstream and Downstream

G Suresh

17 years of industrial experience Working in an automobile MNC

Eg. A person rows a kilometre down the stream in 10 minutes and up the stream in 30 minutes. Find the velocity of the stream. Ans) Speed of the person down the stream = 1 km / 10 minutes = 6 km / hr Speed of the person up the stream = 1 km / 30 minutes = 2 km / hr Let the speed of the man be x... read more

Eg. A person rows a kilometre down the stream in 10 minutes and up the stream in 30 minutes. Find the velocity of the stream.

Ans) Speed of the person down the stream = 1 km / 10 minutes = 6 km / hr

Speed of the person up the stream = 1 km / 30 minutes = 2 km / hr

Let the speed of the man be x km/h, and y km/h be the velocity of the stream

Therefore x + y = 6 and x - y = 2. Solving we get velocity of the stream, y = 2 kmph

**Remember: Upstream means one is rowing against the direction of water flow while downstream means one is rowing in the same direction of water flow.**

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Comments Asked on 31 Mar CBSE/Class 7/Maths CBSE/Class 8/Maths

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Answer

Asked on 19 Mar CBSE/Class 7/Maths CBSE/Class 8/Maths CBSE/Class 9/Mathematics

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Lesson Posted on 24 Feb CBSE/Class 7/Maths

Circular Motions & Typical Time Speed & Distance

Sujoy D.

1. Strong concept building classes. 2. Weekly tests in weak areas for students to improve their confidence. 3....

Question: A father starts from home at 3pm to pick his son from school at 4pm. one day the school got over early at 3pm. The son started walking home. He met his father on way and both returned home fifteen mins earlier than usual time. Speed of father is 35kmperhour. What is the speed of the sun? ... read more

Question:

A father starts from home at 3pm to pick his son from school at 4pm. one day the school got over early at 3pm. The son started walking home. He met his father on way and both returned home fifteen mins earlier than usual time. Speed of father is 35kmperhour. What is the speed of the sun?

Answer:

read less

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Comments Lesson Posted on 24 Feb CBSE/Class 7/Maths CBSE/Class 6/Maths

Circular Motions & Typical Time Speed & Distance

Sujoy D.

1. Strong concept building classes. 2. Weekly tests in weak areas for students to improve their confidence. 3....

Question: A and B run around a circular track at speeds of 7m/s and 11m/s starting from the same point simultaneously in the same direction. At how many distinct points on the track will A and B meet if they run forever ? Answer: As the bodies are moving in same direction hence number of distinct... read more

Question:

A and B run around a circular track at speeds of 7m/s and 11m/s starting from the same point simultaneously in the same direction. At how many distinct points on the track will A and B meet if they run forever ?

Answer:

As the bodies are moving in same direction hence number of distinct points: (11-7) = 4

No the points will be same always as distinct are asked so only 4

Oa : 4

As the bodies are moving in same direction hence number of distinct points: (11-7) = 4

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Comments Lesson Posted on 24 Feb CBSE/Class 7/Maths CBSE/Class 6/Maths

Circular Motions & Typical Time Speed & Distance 3

Sujoy D.

1. Strong concept building classes. 2. Weekly tests in weak areas for students to improve their confidence. 3....

Concept 6: Application of AM-GM in TSD Using AM & HM in proportionality relations,Quite often in questions we find that the given speeds (or time taken) are in an Arithmetic Progression. And if distance covered at the speeds is constant, then time taken (or speeds) will be inversely proportional... read more

Concept 6: Application of AM-GM in TSD

Using AM & HM in proportionality relations,Quite often in questions we find that the given speeds (or time taken) are in an Arithmetic Progression. And if distance covered at the speeds is constant, then time taken (or speeds) will be inversely proportional i.e. they will be in Harmonic Progression.

For those who have forgotten, the Arithmetic Mean of a and b is(a + b)/2 and the Harmonic Mean of a and b is 2ab/(a+b)

Though it requires a little trained eyes to identify the above, it will be useful if you keep a watch for it. See the following data to realise that either time taken or speeds are in an Arithmetic Progression.

E.g: 1. If I travel at 15 kmph, I reach office at 10 am,if I travel at 10 kmph, I reach office at 10:30 am. At what speed should I travel so that I reach office at 10:15. Assume I leave home at same time and take the same route. ( Use am/hm -- no other method)

Solution . Leaving at same time and reaching at 10 am, 10:15 am and 10:30 am suggests that the time travelled are in AP. Thus, speeds are in HP and required speed is the,

HM of 10 & 15

i.e.2 *10 *15/25 = 12 kmph

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Comments Lesson Posted on 24 Feb CBSE/Class 7/Maths

Circular Motions & Typical Time Speed & Distance 6

Sujoy D.

Question: A and B are moving in the same direction with speeds 5 and 11 while C is in moving in the opposite direction at speed 3. If they start together, at how many distinct meeting points they should meet ? Answer: Oa : 2 Solution : A and B in sane direction while C in opposite. So, A and B... read more

Question:

A and B are moving in the same direction with speeds 5 and 11 while C is in moving in the opposite direction at speed 3. If they start together, at how many distinct meeting points they should meet ?

Answer:

Oa : 2

Solution : A and B in sane direction while C in opposite.

So, A and B will have 11 - 5 = 6 distinct meeting points.

A and C will have 3 + 5= 8 distinct meeting points.

B and C will have 11 + 3 = 14 distinct meeting points.

A, B and C will have HCF (6, 8, 14) = 2 distinct meeting points.

They will meet at 2 distinct points on the track

Question:

A , B and C run around a circular track of length 1.2 km at speed of 5m/s , 7m/s and 8m/s respectively starting from the same point simultaneously. While A and C run in the same direction, B runs in the opposite direction .

a) When will all of them meet for first time they start the race ?

b) In the first hour of the race how many more times will B and C meet than the number of times A and B meet .

Answer:

Oa : a) 400, b) 9

a) Let us start by figuring out with A and B will meet for the first time. This is given by => (Track length /Relative Speed )

= 1200/12 = 100 seconds

Now think about when A and C meet for the first time. This is given by 1200/3 = 400 seconds.

B and C will meet for the first time after 1200/15 = 80 seconds

A and B will meet once every 100 seconds or at times 100 .seconds from the start.

A and C will meet every 400 seconds or at times 400 seconds from start

Band C will meet once every 80seconds or at times 80,.....from the start

So all three will meet once every 400 seconds , which is nothing but LCM ( 100,400,80) = 400

b) In an hour B and C will meet 3600/80 => 45 times

In an hour A and B meet 3600/100 => 36 times

So B and C meet 9 times more than A and B do.

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