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

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## (1) Express Each Ratio in Its Simplest Form

(a)

(b)

(c)

(d)

## (2) Tick (β) the Equivalent Ratios and (Γ) if Not

(a)

(b)

## (3) Tick (β) the Equivalent Ratios and (Γ) if Not

(a)

## (4) Tick (β) the Equivalent Ratios and (Γ) if Not

(a)

(b)

(c)

## (5) Find the Value of X

(a)

(b)

## (6) Find the Value of X

(a)

(b)

## (7) Fill the Boxes to Ensure That the Numbers Are in Proportion

(a)

(b)

## (8) Fill the Boxes to Ensure That the Numbers Are in Proportion

(a)

## (9) Fill the Boxes

(a)

## (10) Find the Following Ratios

(a)

(b)

## (11) Find the Following Ratios

(a)

(12) If , find

(13) If , find

## (14) if T: U = V: W, Than Both These Ratio Are Equal to (Tick (β) if ItΥs Correct and (Γ) if Not)

(a)

(b)

(c)

## (15) if T: U = V: W, Than Both These Ratio Are Equal to (Tick (β) if ItΥs Correct and (Γ) if Not)

(a)

(b)

(c)

## (16) if T: U = V: W, Than Both These Ratio Are Equal to (Tick (β) if ItΥs Correct and (Γ) if Not)

(a)

(b)

(c)

## (17) Indicate Whether βAβ is Directly (D) or Inversely (I) Proportional to βBβ . Calculate the Proportionality Constant (K) and Complete the Table

(a)

## (18) Indicate Whether βAβ is Directly (D) or Inversely (I) Proportional to βBβ . Calculate the Proportionality Constant (K) and Complete the Table

(a)

## (19) Indicate Whether βXβ is Directly (D) or Inversely (I) Proportional to βYβ . Calculate the Proportionality Constant (K) and Complete the Table

(a)

## (20) Indicate Whether βXβ is Directly (D) or Inversely (I) Proportional to βYβ . Calculate the Proportionality Constant (K) and Complete the Table

(a)

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

(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?

## (23) Mehul and Vimal Can Together Complete the Work in 30 Days, if Mehul Work Alone Than He Finish the Work in 40 Days, Than Find How Many Days Vimal Take to Complete Work Alone?

## (24) the Inlet Pipe of a Tank Fills It in 3 Hours, While the Outlet Pipe Empties It in 9 Hours. Find the Time Taken to Fill the Tank if Both the Pipes Are Opened Together

## (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.

## Answers and Explanations

### Answer 1 (A)

- We know that
- So
- So,

### Answer 1 (B)

- We know that
- So,
- So,

### Answer 1 (C)

- We know that
- So,
- So,

### Answer 1 (D)

- We know that
- So,
- So,

### Answer 2 (A)

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

### Answer 2 (B)

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

### Answer 3 (A)

- 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,

### Answer 4 (A)

- For first ratio;

- And for second ratio;

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

### Answer 4 (B)

- For first ration;
- And for second ratio;

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

### Answer 4 (C)

- 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,

### Answer 5 (A)

- Given equation,

### Answer 5 (B)

- Given equation,

### Answer 6 (A)

- Given ratio in equation,

### Answer 6 (B)

- Given ratio in equation,

### Answer 7 (A)

- Therefore, the answer is

### Answer 7 (B)

- Therefore, the answer is

### Answer 8 (A)

- Given equation,

- So, the answer is

### Answer 9 (A)

- 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 formΥs denominator so, numerator is also multiplied by 3 to the simplest formΥs numerator.
- Now guess that numerator of simplest form is 3 than ,
- First ration should be,

- Now for second ration;

- So answer is,

- 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.

### Answer 10 (A)

- 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

### Answer 10 (B)

- 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

### Answer 11 (A)

- Given ratio,
- So,

- Here βuβ is common in both the ratio, so we multiply both the ration by such a number that value of βuβ 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

### Answer (12)

- 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,

### Answer (13)

- To get numerator of
- Subtract denominator from numerator;

- To get denominator of
- Add denominator in numerator;

- Divide numerator by 5 to get required denominator;

- Inverse the ratio;

- Now from eqution-1;

- Now from equation 2 and equation-3

### Answer 14 (A)

- Here given

- So,
- Now,

- Therefore, the answer is

### Answer 14 (B)

- Here given

- So,
- Now,

- Therefore, the answer is

### Answer 14 (C)

- Here given

- So,
- Now,

- Therefore, the answer is

### Answer 15 (A)

- Here given

- So,
- Now,

- Hence, the answer is

### Answer 15 (B)

- Here given

- So,
- Now,

- Hence, the answer is

### Answer 15 (C)

- Here given

- So,
- Now,

- Hence, the answer is

### Answer 16 (A)

- Here given

- So,

- Now,

- Hence, the answer is

### Answer 16 (B)

- Here given

- So,

- Now,

- Hence, the answer is

### Answer 16 (C)

- Here given

- So,

- Now,

- Hence, the answer is

### Answer 17 (A)

- Here from given data it is clear that as the value of βaβ increase from 4 to 24 and parallel the value of βbβ 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

### Answer 18 (A)

- Here from given data it is clear that as the value of βaβ increase from 10 to 20 and parallels the value of βbβ 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;

### Answer 19 (A)

- Here from given data it is clear that as the value of βxβ increase from 20 to 100and parallel the value of βyβ 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;

### Answer 20 (A)

- Here from given data it is clear that as the value of βxβ decrease from 50 to 10; the value of βyβ 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;

### Answer 21 (A)

- 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,

### Answer 21 (B)

- 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 .

### Answer 21 (C)

- 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

### Answer 22 (A)

- 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.

### Answer 22 (B)

- 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**.

### Answer (23)

- 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**.

### Answer (24)

- 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**.

### Answer 25 (A)

- 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**.

### Answer 25 (B)

- Speed of boat in still water
- Stream water speed is 5 km/h
- If boat travel in downstream, than stream speed help boat to increase its speed.

- Hence, if boat travel 50 km downstream, than its average speed for is
**35 km/h**.