Grade 8 Ratio and Variation Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(12) If , find

(13) If , find

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(21) the Population of Bacteria (P) in Water Varies Inversely as the Temperature of Water (T) . If There Are 8,00, 000 Bacteria at 50˚C

(a) Find the relation between population and temperature?

(b) Find the population at

(c) Find the temperature at which their population is ?

(22) if 10 People Can Finish Digging a Well in 8 Days

(a) Find the number of people required to dig a well in 4 days.

(b) How many days will 8 people take to dig the well?

(25) a Boat, Whose Speed in Still Water is 30 Km/H, Travels 75 Km Upstream in 3 Hrs

(a) Find the speed of the stream

(b) If boat travel 50 km downstream, find its average speed for the whole journey.

• We know that
• So
• So,

• We know that
• So,
• So,

• We know that
• So,
• So,

• We know that
• So,
• So,

• Here given two ratio are
• From ratio it is clear that
• So both ratio are not equivalent
• So,

• For first ratio
• And second ratio is
• So, both ratios are equivalent.

• Given ratio,

• For first ratio,
• We know that
• So,
• Now,

• For second ratio,

• We know that
• So,
• Now,

• From above both ration it is clear that, both ratio are not equivalent,

• For first ratio;

• And for second ratio;

• So from above its clear that both ratio are equivalent
• So,

• For first ration;
• And for second ratio;

• From above both ration it is clear that, both ratio are not equivalent,

• For first ratio;
• We know that
• So,

• For second ratio;

• We know that
• So,

• From above both ration it is clear that, both ratio are not equivalent,

• Given equation,

• Given equation,

• Given ratio in equation,

• Given ratio in equation,

• Given equation,

• Given proportion,

• Denominator of left hand side ratio is 6 and
• Factor of 6 are
• Denominator of right hand side ratio is 8 and
• Factor of 8 are
• Here we can see that 2 is common in both ratio denominator.
• And for equivalent of ration it is compulsory that simplest form both ratio should be same.
• Now for first ration denominator multiplied by 3 to the simplest form՚s denominator so, numerator is also multiplied by 3 to the simplest form՚s numerator.
• Now guess that numerator of simplest form is 3 than ,
• First ration should be,

• Now for second ration;

• NOTE:- this answer is right based on our guess numerator of simplest form, If someone guess another numerator of simplest form than answer may change.

• So,

• Here b is common in both the ratio, so we multiply both the ration by such a number that value of b in both ratio will be same,
• For that if we multiply first ration by 2 and second ratio by 1 than we have a same b value in both ration
• So,

• So, we can write that

• So,

• Here n is common in both the ratio, so we multiply both the ration by such a number that value of n in both ratio will be same,
• For that if we multiply first ratio by 1 and second ratio by 3 than we have a same value of n in both ratio
• So,

• So, we can write that

• Given ratio,
• So,

• Here “u” is common in both the ratio, so we multiply both the ration by such a number that value of “u” in both ratio will be same,
• For that if we multiply first ratio by 5 and second ratio by 8 than we have a same value of u in both ratio
• So,

• Now,

• So, we can write that

• Now to get numerator of

• Now, add denominator in numerator to get required numerator.

• Now divide denominator by 2

• Now to get denominator of

• Multiply numerator by 2,

• Now subtract denominator from numerator,

• Inverse ratio

• Now from equation-1 and equation-2,

• To get numerator of
• Subtract denominator from numerator;

• To get denominator of

• Divide numerator by 5 to get required denominator;

• Inverse the ratio;

• Now from eqution-1;

• Now from equation 2 and equation-3

• Here given

• So,
• Now,

• Here given

• So,
• Now,

• Here given

• So,
• Now,

• Here given

• So,
• Now,

• Here given

• So,
• Now,

• Here given

• So,
• Now,

• Here given

• So,

• Now,

• Here given

• So,

• Now,

• Here given

• So,

• Now,

• Here from given data it is clear that as the value of “a” increase from 4 to 24 and parallel the value of “b” also increase from 5 to 30,
• Hence we can say that a is directly proportion to b
• Hence

• Now, from given data ; for a

• Now from given data ; for b

• Now, from given data ; for a

• Here from given data it is clear that as the value of “a” increase from 10 to 20 and parallels the value of “b” Decrease from 200 to 100,
• Hence we can say that a is inversely proportion to b
• Hence

• Now from given data than for b;

• Now from given data than for a;

• Now from given data than for b;

• Here from given data it is clear that as the value of “x” increase from 20 to 100and parallel the value of “y” also increase from 40 to 200,
• Hence we can say that x is directly proportion to y
• Hence

• Now from given data than for y;

• Now from given data than for x;

• Now from given data than for y;

• Here from given data it is clear that as the value of “x” decrease from 50 to 10; the value of “y” increase from 20 to 100,
• Hence we can say that x is inversely proportion to y
• Hence,

• Now from given data than for y;

• Now from given data than for x;

• Now from given data than for y;

• The population of bacteria in water varies inversely as the temperature of water
• Means

• Now at temperature C the population of bacteria is 8,00, 000
• So,

• Relation between population of bacteria (p) and water temperature (t) is as below,

• When water temperature (t) is C than to find out population of bacteria (p)

• When water temperature (t) is C than population of bacteria (p) is .

• When population of bacteria (p) is 3,00, 000 than to find out water temperature (t) ;

C

• When population of bacteria (p) is 3,00, 000; water temperature (t) is C

• Here well digging work completed in number on days (d) inversely proportion to number of people (n) engaged.
• Hence we can say that,

• 10 people (n) can finish digging a well in 8 days (d) ,

So,

• So,

• Now, number of people (n) required to dig the well in 4 days (d) is,

• Therefore, 20 people required to dig the well in 4 days.

• How many days (d) will 8 people (n) take to dig the well.

• Hence, 8 numbers of people can dig a well in 10 days.

• If Mehul work alone than he finish the work in 40 days.
• So in one day he can do of work.
• Now if Mehul and Vimal work together than they complete the work in 30 days,
• So, they complete of work in a day.
• Hence we can say that,

• So in a day Vimal can complete of the work

• So if Vimal work alone to complete the work than he will take 120 Days.

• Inlet pipe of tank fills the tank in 3 hours.
• So in one hour pipe fill of the tank.
• Now, if we open the outlet pipe of a tank than it will take 9 hours to empty it.
• So in one hour outlet pipe empty of tank.
• Now if tank was empty and we start both the pipe (inlet and outlet) at the same time than in our tank fill by,

• Here we take minus sign for empty of tank , because it decrease the water level when we open the outlet pipe
• Hence in one hour tank fill by

• if tank was empty and we start both the pipe (inlet and outlet) at the same time than in tank fill by in a hour.

• So, if tank was empty and we start both the pipe (inlet and outlet) at the same time than it will take 4.5 hours to fill the tank.

• Speed of boat in still water
• In upstream boat travel 75 km in 3 hour
• So , boat speed in upstream

• Here we take minus sign for upstream water because it decreases the speed of boat.

• Hence, stream speed is 5 km/h.