September 10, 2024

# Ratio and proportion class 6

In our daily life, many  times we compare two quantities of the same type.  The comparison by division is the Ratio.
when we compared the two quantities in terms of ‘how many times’. This comparison is known as the Ratio. We denote
ratio using symbol ‘:’ .

Example : Cost of a pen is Rs. 10 and cost of a pencil is Rs. 2. How many times the cost of a pen that of a pencil? Obviously it is five times.

The ratio of the cost of a pen to the cost of a pencil = $\frac{10}{2}=&space;\frac{5}{1}=&space;5:&space;1$

If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’ to equate the two ratios.

## Ratio and proportion class 6 extra questions with answers

1) Raj purchased 3 pens for Rs. 15 and Anu purchased 10 pens for Rs. 50. Whose pens are more expensive?
Solution : Ratio of number of pens purchased by Raj to the number of pens purchased by Anu = 3 : 10.
Ratio of their costs = 15 : 50 = 3 : 10
Both the ratios 3 : 10 and 15 : 50 are equal. Therefore, the pens were purchased for the same price by both.

2) Express the following in terms of ratios
(i) The length of rectangle is double of its breadth.
Solution :
Let the breadth be x . Then  length = 2x.
Ratio of length and breadth = $\mathrm{\frac{2x}{x}}&space;=\frac{2}{1}=&space;2&space;:&space;1$

(ii) The quantity of acid in the diluted acid is $\frac{2}{3}$ of the water.
Solution:
Let the quantity of water be x. Then quantity of acid is $\mathrm{\frac{2}{3}x}$

.
Ratio of acid and water = $\mathrm{\frac{\frac{2}{3}x}{x}}$ =$\frac{2}{3}$

To dilute  an acid , mix acid and water in the ratio 2 : 3 .

3) Express the ratio 150 : 400 in its simplest form .
Solution :
To express the ratio 150:400 in its simplest form, you need to find the greatest common factor (GCF) of the two numbers and then divide both numbers by that factor.
The GCF of 150 and 400 is 50. Dividing both numbers by 50.

$\frac{150}{400}=\frac{150\div&space;50}{400\div&space;50}=\frac{3}{8}=&space;3&space;:&space;8$

So, the simplified form of the ratio 150:400 is 3:8 .

4) Find the ratio of 200grams to 4 kg .
Solution :
To find the ratio of 200 grams to 4 kilograms, you need to make sure that the units are the same. Since 1 kilogram is equal to 1000 grams, you can express 4 kilograms as 4000 grams.
The ratio of 200 grams to 4000 grams is 200 : 4000 .
Now, simplify the ratio by finding the greatest common factor (GCF) of 200 and 4000, which is 200.
Divide both numbers by the GCF.

$\frac{200}{4000}=\frac{200\div&space;200}{4000\div&space;200}=\frac{1}{20}$

So, the ratio of 200 grams to 4 kilograms is 1:20.

5) The number of boys and girls in a school are 480 and 384 respectively .Express the ratio of the number of boys to that of the girls in the simplest form .
Solution :
To express the ratio of the number of boys to the number of girls in the simplest form, you can find the greatest common factor (GCF) of the two numbers and then divide both by that factor.
Number of boys = 480  and  Number of girls = 384
Ratio =  $\frac{480}{340}$

The HCF of 480 and 340  is 96 . Dividing numerator and denominator  by 96 .
$\frac{480}{384}=&space;\frac{480\div&space;96}{384\div&space;96}$

=  $\frac{5}{4}$
So, the ratio of the number of boys to the number of girls in simplest form is 5:4.

6)  Find the ratio of the price of coffee to that of tea , when coffee costs Rs .24 per 100gm and the tea costs Rs. 80 per kg.
Solution :
Cost of 100 gm of coffee = Rs. 24
$\Rightarrow$

Cost of 1 gm of coffee = Rs. $\frac{24}{100}$
$\Rightarrow$
Cost of 1000 gm of coffee = Rs. $\frac{24}{100}\times&space;1000&space;=&space;Rs.&space;240$
$\therefore$
Cost of 1 kg of coffee = Rs.  240
Cost of 1 kg of tea = Rs. 80
Ratio = $\frac{240}{80}=&space;\frac{3}{1}$
Ratio of the price of coffee to that of tea =3 : 1

7)  If A : B  = 3 : 4 ,  B : C = 5 : 6 and C : D = 11 : 9, then find the ratio of A : D .
Solution :  $\frac{A}{D}=\frac{A}{B}\times&space;\frac{B}{C}\times&space;\frac{C}{D}$

=$\frac{3}{4}&space;\times&space;\frac{5}{6}\times&space;\frac{11}{9}$

=$\frac{55}{72}$

$\Rightarrow$ A 😀 = 55 : 72

8) Two numbers are in the ratio 2 : 3. If 9 is added to each, they will be in the ratio 3 : 4. Find the numbers.
Solution :  Let numbers be $2x$

and $3x$ . Then $\frac{2x+9}{3x+9}&space;=&space;\frac{3}{4}$

$\Rightarrow&space;4(2x+9)=&space;3(3x+9)$
$\Rightarrow&space;8x+36=&space;9x+27$

$\Rightarrow&space;x=&space;36-27=&space;9$
Hence 1st numbers  = 2 x 9 = 18
Second number = 3 x 9 = 27

9) A B, and C divide an amount of Rs. 9861 amongst themselves in the ratio of 3 : 11  : 5  , respectively. What is the B’s share in the amount?
Solution :  B’s share = $\mathrm{\frac{ratio\,&space;term&space;\,&space;of&space;\,&space;B}{total&space;\,&space;sum&space;\,&space;of&space;\,&space;ratios}}\times&space;total&space;\,&space;amount$

$=\frac{11}{19}\times9861$

= Rs. 5709

10) What must be subtracted from each term of the ratio 3 : 2. So, that the ratio becomes 2 : 5 ?

Solution: Let x is to be subtracted. Then  $\frac{3-x}{7-x}=\frac{2}{5}$

$\Rightarrow&space;15-5x=14-2x$

$\Rightarrow&space;15-14=&space;5x-2x$

$\Rightarrow&space;1&space;=3x$

$\Rightarrow&space;x=\frac{1}{3}$

11) The ratio of boys to girls in a class is 3:4. If there are 15 boys, how many girls are there?
Solution
:  Let the number of girls be x . Then $\frac{number\,&space;\,&space;of\,&space;\,&space;boys&space;}{&space;number&space;\,&space;\,&space;of&space;\,&space;\,&space;girls}&space;=&space;\frac{3}{4}$ (Since the ratio of boys to girls is 3:4)

$\Rightarrow&space;\frac{15}{x}&space;=\frac{3}{4}$

$\Rightarrow&space;3x=60$

$\Rightarrow&space;x=\frac{60}{3}=20$

Therefore, the number of girls is .

12) A recipe calls for a ratio of 2 cups of flour to 3 cups of sugar. If you want to make half the recipe, how much flour should you use?
Solution: Since you want to make half the recipe, you need to find half of each part of the ratio. Half of 2 cups is 1 cup. Therefore, you should use 1 cup of flour.

13) The length of a rectangle is in the ratio 5:8 to its width. If the width is 6 meters, find the length of the rectangle.
Solution: Let the length of the rectangle is x.
Since the ratio of length to width is 5:8 , this implies $\frac{x}{6}=\frac{5}{8}$
$\Rightarrow&space;8x=30$

$\Rightarrow&space;x=\frac{30}{8}=3.75$

Therefore the length of the rectangle is 3.75 units.

### Ratio sums for class 6 (unsolved with answers )

(1) If p : q = 3 : 4 and q  : r = 8 : 9. Find p: q: r .

(2) 3 : 5 :: 60 : x, find the value of x.

3) If A  : B = 6  : 7 and B : C = 8 : 9, then find A : C .

4) What is ratio in between 7 months and 7 yr?

5)Divide Rs. 4000 among A , B and C so that their shares may be in the ratio of 5  : 7  : 8 .

6)The ratio of two numbers is 3  : 8 and their difference is 116. What is the largest number?

7)What must be added to each term of the ratio 49 : 68, so that it becomes 3 : 4?

8) The sum of the squares of three numbers is 116 and their ratio is 2 : 3 : 4. Find the numbers.

9) A sum of money is to be distributed between Ajay and Sanjay in the proportion of 7 : 11, respectively. Sanjay gets Rs.6000
more than Ajay. How much did Ajay get?

10) The ratio of copper and zinc is 11: 6. How much zinc is there in 850 kg of brass?

11)If x  : y = 7 : 5, then  find the value of $\frac{5x-2y}{3x+2y}$

.

12)A picture is 60 cm wide and 1.8 m long.  Find the ratio of its width to its perimeter.

13)Neelam’s annual income is Rs. 288000. Her annual savings amount to Rs. 36000.  Find the ratio of her savings to her expenditure.

14) On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3. If there are 18 books with green cover, then find the number of books with brown cover.

15) If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then the ratio of the distance travelled by them in one hour is

Ans. 1) 6 : 8 : 9    2)100   3) 16 : 21  4)  1 : 12   5)  Rs. 1000, Rs.1400,  Rs.1600   6) 184  7)8     8) 8 ,12 , 6  9) Rs. 10500  10) 300kg    11) $\frac{25}{31}$

12) 1 : 8  13) 1 : 7    14)  27   15) 5 : 8

Ratio and proportion extra questions for class 6 pdf