MCQ on Ratio and Proportion for Class 6

Answer: (b) 11 : 36

Explanation: HCF of 33 and 108 is 3

Since, 33 : 108

= 33/108

Dividing Both 33 and 108 by their HCF

= (33÷3)/(108÷3)

= (11÷36)

= 11 : 36

Hence, the simplest form of 33 : 108 is 11 : 36

Answer: (d) 1 : 2

Explanation: Taking both the quantities in same unit, we have

1.9 m = ( 1.9 x 100 ) = 190 cm

The equation now becomes, 95 cm : 190 cm

or

= 95/190

Dividing both the numbers by their HCF, i.e.,

= (95÷95)/(190÷95)

= 1/2 = 1 : 2

Hence, the required ratio is 1 : 2

Answer: (b) 1 : 25

Explanation: Taking both the quantities in same unit, we have

1.2 kg = ( 1.2 x 1000 ) = 1200 g

The equation now becomes 48 g : 1200 g

or

= 48/1200

Dividing both the numbers by their HCF, i.e., 48

= (48÷48)/(1200÷48)

= 1/25= 1 : 25

Hence, the required ratio is 1 : 25

Answer: (b) 1 : 3

Explanation: Taking both the quantities in same unit, we have

3 hours = ( 3 x 60 ) = 180 min

The equation now becomes 60 min : 180 min

or

= 60/180

Dividing both the numbers by their HCF, i.e., 60

= (60÷60)/(180÷60)

= 1/3 = 1 : 3

Hence, the required ratio is 1 : 3

Answer: (a) 1 : 3

Explanation: Taking both the quantities in same unit, we have

₹ 2.4 = ( 2.4 x 100 ) = 240 paise

The equation now becomes 80 paise : 240 paise

or

= 80/240

Dividing both the numbers by their HCF, i.e., 80

= (80÷80)/(240÷80)

= 1/3= 1 : 3

Hence, the required ratio is 1 : 3

Answer: (b) 10/30

Explanation: On multiplying or dividing each term of a ratio by the same non zero number, we get a ratio equivalent to the given ratio

For, 10/30

Both numerator and denominator of given fraction is multiplied by same nonzero number i.e., 5.

(2×5)/(6×5) = 10/30

10/30 is an equivalent ratio of 2/6.

6/2 is not an equivalent ratio of 2/6 As both 2 and 6 are not multiply by same non zero number.

11/18 is not an equivalent ratio of 2/6 As both 2 and 6 are not multiply by same non zero number.

10/18 is not an equivalent ratio of 2/6 As both 2 and 6 are not multiply by same non zero number.

Answer: (b) 28 and 63

Explanation: Let the required number be 4a and 9a

Since the sum of these two numbers is given, we can say that

4a + 9a = 91

13a = 91

a = 91/13

a = 7

So, the first number is 4a = 4 x 7

= 28

Second number is 9a = 9 x 7

= 63

Hence, two numbers are 28 and 63.

Answer: (a) X = 3500 , Y = 2000

Explanation: Total money = ₹ 5500

Given ratio = 7 : 4

Sum of ratio terms = ( 7 + 4 )

= 11

Give: 7/11part of ₹ 5500 to X

Give: 4/11part of ₹ 5500 to Y

that is,

X ‘s share = ₹ ( 5500 x (7/11)) = ₹ 3500

Y ‘s share = ₹ ( 5500 x (4/11)) = ₹ 2000

Answer: (b) X = 2175 , Y = 4350 , Z = 725

Explanation: Total money = ₹ 7250

Given ratio = 3 : 6 : 1

Sum of ratio terms = ( 3 + 6 + 1 )

= 10

X share = ₹ ( 7250 x (3/10)) = ₹ 2175

Y share = ₹ ( 7250 x (6/10)) = ₹ 4350

Z share = ₹ ( 7250 x (1/10)) = ₹ 725

Answer: (a) ( 4 : 5 ) > ( 3 : 7 )

Explanation: We can write

( 4 : 5 ) = 4/5 and ( 3 : 7 ) = 3/7

Now, let us compare 4/5 and 3/7

LCM of 5 and 7 is 35

Making the denominator of each fraction equal to 35

We have, 4/5 = (4×7)/(5×7) = 28/35

and 3/7 = (3×5)/(7×5) = 15/35

In case of Like fractions, the number whose numerator is greater is larger. Hence we can say (28/35) > (15/35)

That is (4/5) > (3/7)

Hence, ( 4 : 5 ) > ( 3 : 7 )

Answer: (c) 5

Explanation: Let 1/7 = y/35

Then, 1 x 35 = 7y

7y = 1 x 35

y = (1×35)/7

y = 5

Hence, 1/7 = 5/35

Answer: (d) 11 , 184

Explanation: Let (44/92) = (y/23)

Then, 44 x 23 = 92y

92y = 44 x 23

y = (44×23)/92

y = 11

Since, (44/92) = (11/23)

Again, let 1123 = 88z

Then, 11z = 88 x 23

z = (88×23)/11

z = (2024)/11

z = 184

Since, (11/23) = (88/184)

Hence, (44/92) = (11/23) = (88/184)

Answer: (b) No

Explanation: We have 20 m : 60 m

= 20 : 60

= 20/60

=(20÷20)/(60÷20) (HCF of 20 and 60 is 20 )

= 1/3

60 km : 240 km

= 60 : 240

= 60/240

=(60÷60)/(240÷60) ( HCF of 60 and 240 is 60 )

= 1/4

Since, the ratios 20 m : 60 m and 60 km : 240 km are equal to 1/3 and 1/4 respectively . So, they are not in proportion.

Answer: (a) Yes

Explanation: We have, 8 : 6 = 8/6 = (8÷2)/(6÷2)= 4/3

and 12 : 9 = 12/9 = (12÷3)/(9÷3)= 4/3

Since, 8 : 6 = 12 : 9

Hence, 8 , 6 , 12 , 9 are in Proportion

Alternative method: Product of extremes = Product of means

Here, Means are 6 and 12

Extremes are 8 and 9

Product of extremes = 8 x 9 = 72

Product of means = 6 x 12 = 72

Since, Product of extremes = Product of means

Hence, 8 , 6 , 12 , 9 are in Proportion

Answer: (c) 4

Explanation: We know that, Product of means = Product of extremes

In the given numbers, we can say that 3 , y are means and 6 , 2 are extremes

3 x y = 6 x 2

y = (6×2)/3

y = 4

Hence, y = 4

Answer: (c) 20

Explanation: Clearly, Product of means = Product of extremes

y x y = 40 x 10

y² = 40 x 10

y² = 400

Hence, y = 20

Answer: (c) 75

Explanation: 3 , 15 , y are in proportion

Which means 3 , 15 , 15 , y are in proportion

i.e., 3 : 15 : : 15 : y

Product of means = Product of extremes

here,

means = 15 and 15

extremes = 3 and y

15 x 15 = 3 x y

225 = 3 x y

y = 225/3

Hence, y = 75

Answer: (d) 10 : 11

Explanation: Number of girls/Number of boys = 80/88

On simplifying,

Number of girls/Number of boys = (80÷8)/(88÷8) ( HCF of 80 and 88 is 8 )

= 10/11= 10 : 11

Hence, the ratio is 10 : 11

Answer: (b) 45 days

Explanation: Clearly, less men will take the more days.

And, more men will take less days.

30 men can reap a field in = 15 days

1 man can reap a field in = ( 15 x 30 ) days

Hence, 10 men can reap a field in = (15×30)/10 days = 45 days

Hence, 10 men can reap a field in 45 days.

Answer: (c) ₹ 5

Explanation: Cost of 36 bananas = ₹ 18

Cost of 1 banana = ₹ 18/36

Cost of 10 bananas = ₹ (18×10)/36

= ₹ 5

Answer: (b) ₹ 15400

Explanation: Earning on 19 cars = ₹ 13300

1 car = ₹ 13300/19 = ₹ 700

Earning on 22 cars = ₹ ( 700 x 22 )

= ₹ 15400

Answer: (a) ₹ 4900

Explanation: Annually means 1 year = 12 months

Fees of 12 month = ₹ 58800

Fees of 1 month = ₹ 58800/12

= ₹ 4900