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## Karnataka 2nd PUC Basic Maths Question Bank Chapter 7 Ratios and Proportions Ex 7.1

Part – A

2nd PUC Basic Maths Ratios and Proportions Ex 7.1 One Mark Questions and Answers ( 1 × 10 = 10)

Question 1.
If 3:5 is a ratio, find the antecedent and consequent.
Antecedent = 3, Consequent = 5.

Question 2.
x gets a salary of7 20,000, y gets a salary of 5,000. Find the ratio of their salaries.
Ratio of their salaries is 20000:50000 = 2:5.

Question 3.
Find the inverse ratio of 4:5.
Inverse ratio of 4 : 5 is 5 : 4

Question 4.
A house consumes 30 kgs of wheat and 4kg of sugar compare the consumption of wheat and sugar in the form of ratio.
Wheat: Sugar = 30 kg: 4 kg = 15:2. 6.

Question 5.
Mr. X completes a job is 3 hours and Mr. Y completes the same job is 45 minutes compare their performances.
3 hrs.: 45 minutes = 3 × 60 : 45 = 180 : 45
= 4:1.

Question 6.
Find the compound ratio of 3 : 4 and 4: 7.
Compound ratio = $$\frac{3}{4} \cdot \frac{4}{7}=\frac{3}{7}=3: 7$$

Question 7.
Find the compound ratio of 1:2, 2:3 and 3:5.
Compound ratio = $$\frac{1}{2} \times \frac{2}{3} \times \frac{3}{5}=\frac{1}{5}=1: 5$$

Question 8.
Find the duplicate ratio of 5 : 4.
Duplicate ratio of 5 : 4 is 52: 42 = 25: 16.

Question 9.
Find the triplicate ratio of 3 : 5.
Triplicate ratio of 3 : 5 is 33: 53 = 27 : 125.

Question 10.
Find the subduplicate ratio of 9:49.
Subduplicate ratio of 9 : 49 is √9:√49 = 3:7

Question 11.
Find the subtriplicate ratio of 125: 64.
Subtriplicate ratio of 125 : 64
= 3√125:3√64 = 5:4

Question 12.
Find the value of x of 5 : 20 = 3 :x.
5x = 20 x 3⇒ x = $$\frac{20 \times 3}{5}=$$ = 12 ⇒ X = 12

Part – B

2nd PUC Basic Maths Ratios and Proportions Ex 7.1 Two Marks Questions and Answers (2 × 10 = 20)

Question 1.
Find the ratio between two numbers such that their sum is 40 and their difference is 8.
Let the two numbers be x & y
Given x + y = 40 ……. (1)
& x – y = 8 … (2)
Solving we get
Adding 2x = 48 ⇒ x = 24 & y = 40 – 24 = 16
∴Ratio of the numbers is 24 : 16 ⇒ 3:2.

Question 2.
A ratio is the lowest term is 3:8. If the difference between the quantities is 25. Find the quantities.
Let the numbers are 3x and 8x
Given 8x – 3x = 25
5x = 25 ⇒ X = 5
∴ Two numbers are 3(5) & 8(5)
i.e., 15 and 40.

Question 3.
Two numbers are is the ratio 3:5. If 5 is added to each , they are is the ratio. 2:3 find the numbers.
Let two numbers be 3x & 5x
If 5 is added to each then $$\frac{3 x+5}{5 x+5}=\frac{2}{3}$$
9x + 15 = 10x + 10
x = 5
∴ The two numbers are 3(5) & 5(5) = 15 & 25.

Question 4.
What must be added to each term is the ratio 2 : 3 so that is becomes 5:6.
Let x must be added to each term of 2 : 3 then
$$\frac{2+x}{3+x}=\frac{5}{6}$$
⇒ 12 + 6x = 15 + 5x
x = 3.

Question 5.
What must be added to each term is the ratio 4:5 so that is becomes 7:8.
Let x must be added to each of 4:5 then
$$\frac{7-x}{4-x}=\frac{5}{2}$$
x = 3

Question 6.
What must be subtracted from each term is the ratio 7:4 so that it becomes 5:2.
Let x must be subtracted from each of 7 : 4 then $$\frac{7-x}{4-x}=\frac{5}{2}$$
⇒ 14 – 2x = 20 – 5x 5x – 2x = 20 – 14
3x = 6 ⇒ x= 2.

Question 7.
What must be subtracted from each term is the ratio 8:7 so that it becomes 4:3.
Let x must be subtracted from each of 8:7 then
$$\frac{8-x}{7-x}=\frac{4}{3}$$
24 – 3x = 28 – 4x
4x – 3x = 28 – 24
x = 4

Question 8.
If a: b = 2:3, b:c=3:5 and c:d= 5:7 find a:d.

Question 9.
If a: b = 2:3 and b:c= 6:13 find a:b:c.
Given
$$\frac{a}{b}=\frac{2}{3}, \frac{b}{c}=\frac{6}{13}$$
$$\frac{a}{b}=\frac{2 \times 2}{2 \times 2}=\frac{4}{6}$$
∴ a:b:c = 4 : 6 : 13

Question 10.
If a : b = 3:4, b:c=8 = 15 find a:b:c.
$$\frac{a}{b}=\frac{3}{4}, \frac{b}{c}=\frac{8}{15}$$
$$\frac{a}{b}=\frac{3 \times 2}{4 \times 2}=\frac{6}{8} \frac{b}{c}=\frac{8}{15}$$
∴ a : b : c = 6 : 8 : 15

Part-C

2nd PUC Basic Maths Ratios and Proportions Ex 7.1 Three Marks Questions and Answers (3 × 16 = 48)

Question 1.
Divide 1800 is the ratio 3 : 4 : 5.
Sum of the ratios 3 + 4 + 5 = 12
∴  $$\frac{3}{12}$$ × 1800 = 450
$$\frac{4}{12}$$1800 = 600
$$\frac{4}{12}$$1800 = 750

Question 2.
If x : y = 3; 4 find $$\frac{2 x^{2}+3 y^{2}}{x^{2}+y^{2}}$$

Question 3.
If a:b= 2:3 and x:y = 4:7.
Find $$\frac{5 a x+4 b y}{8 a x+3 b y}$$

Question 4.
The angles of a triangle are in the ratio 3:4:5. Find the angles.
Sum of the ratios 3 + 4 + 5 = 12
W. K. T sum of the angles of a triangle = 75°
∴  $$\frac{3}{12}$$ × 180 = 45°, 12
$$\frac{3}{12}$$ × 180 = 60°,
$$\frac{3}{12}$$ × 180 = 75°
∴ The three angles of a triangle are 45°, 60°, 75°

Question 5.
An article is sold at 40% gain an the cost price. Find the ratio of the selling price and cost price.
An article is sold at 40% gain
100 + 40 = 40
If the cost price is 100 then the selling price 100 + expenditure is 4x – 1000 40 = 140
∴ $$\frac{S P}{C P}=\frac{140}{100}=\frac{7}{5}$$
∴ SP : CP = 7 : 5

Question 6.
If the monthly incomes of A and B are is the ratio 3:4 and their expenditures are is the ratio 1 :2. If each saves 1000 find the monthly incomes.
Let monthly income of A is 3x and expenditure
is 3x – 1000 and monthly income of B is 4x and
Given $$\frac{3 x-1000}{4 x-1000}=\frac{1}{2}$$
6x – 4000 = 4x – 2000
⇒ 2x = 2000 ⇒ x = 1000
∴ The monthly income of A = 3x = 3 × 1000 = 3000
∴ The monthly income of B is 3(500) = 2000.

Question 7.
If the monthly incomes of A and Bare in the ratio 3:4 and their expenditure are in the ratio 1:2.If each saves 2000. Find their monthly incomes.
Let their monthly incomes are 3x and 4x and their expenditure are 3x – 2000 and 4x – 2000
Given difference of their squares is $$\frac{3 x-2000}{4 x-2000}=\frac{1}{2}$$
6x – 4000 = 4x – 2000
⇒ 2x = 2000 ⇒ x = 1000
The monthly income of A = 3x = 3 × 1000 = 3000
The monthly income of B = 4x = 4 x 1000 = 4000

Question 8.
Two numbers are is the ratio 6:7. If the difference of their squares is 117 find the two numbers.
Let the two numbers are 6x and 7x
i.e., (7x)2 – (6x)2= 117
49x2 – 36x2= 117
13x2 = 117
⇒ x = 6
∴ The numbers are 3(6) and 46) = 18 and 21.

Question 9.
Two numbers are is the ratio 3:4. If the sum of their squares is 900 find the two numbers.
Given $$\frac{x}{y}=\frac{3}{4}, \frac{y}{z}=\frac{7}{9}$$
Given sum of their squares = 900
(3x)2 + (4x)2= 900
9x2 + 16x2 = 900
25x2 = 900
⇒ x2 = $$\frac{900}{25}$$ = 36 ⇒ x = 6
∴ The numbers are 3(6) and 4 (6) = 18 and 24

Question 10.
If x:y= 3:4 and y:z= 7:9. Find x:y:z.

Part – D

2nd PUC Basic Maths Ratios and Proportions Ex 7.1 Five Marks Questions and Answers (5 × 16 = 80)

Question 1.
Divide ₹ 800 is three parts such that three times of the first, five times of the second and six times the third are equal.
Let the 3 parts be x, y and z
Given 3x = 5y = 62
Let 3x = 6z and 5y = =$$\frac{6}{5}$$z
x = 2z, y = 2
∴ x : y : z = 2z : $$\frac{6}{5}$$z : z= 10:6:5
Sum of the ratios = 10 + 6 + 5 = 21

Question 2.
Divide ₹ 3262 among x, y and z such that if  ₹35, ₹15 and ₹12 are deducted from their respective shares, the remainders are in the ratio 3:5:8.
x + y + z = 3262 and x – 35:y – 15: Z – 12 = 3:5:8 x-35 3 y-155 y -15 5

5x – 175 = 3y – 45,
5x – 3y = 130,
5x = 130 + 3y,
x= 26+$$\frac{3}{5}$$y
8y – 120 = 52 – 60
8y – 5z = 60
5z = 8y – 60
z = $$\frac{8}{5}$$y – 12
Substitute for x and z
Buty x + y + z = 3262

= 26 + 609
x = 635
x = 635, y = 1015 and z = 1612
z = 1624 – 12
z = 1612

Question 3.
If x:y= 2:3. Find the value of $$\frac{2 x^{3}+3 y^{3}}{x^{3}+y^{3}}$$

Question 4.
Divide 5880 is to three parts, such that ‘B’ receive thrice as ‘A’ and C receives $$\frac{5^{t h}}{6}$$ of what B receives.
Let A receive ₹x and B receives ₹ 3x and C receive $$\frac{5}{6}$$(3x) = $$\frac{5}{2}$$x
∴ A:B:C= 1:3:$$\frac{5}{2}$$= 2:6:5
∴ A’s share = $$\frac{2}{13}$$ × 5880 = 904.6
B’s share = $$\frac{6}{13}$$ x 5880 = 2713.8 :
C’s share = $$\frac{5}{13}$$x 5880 = 2261.5

Question 5.
If $$\frac{2 x^{2}+3 y^{2}}{x^{3}+y^{2}}=\frac{2}{41}$$ Find x:y.

Question 6.
Divide 6000 into three parts is the ratio $$\frac{1}{2}: \frac{1}{3}: \frac{1}{6}$$
Given $$\frac{1}{2}: \frac{1}{3}: \frac{1}{6}$$ multiply by 6, we get 3:2:1
1st part = $$\frac{3}{6}$$ × 6000 = 3000
2nd part = $$\frac{3}{6}$$ × 6000 = 2000
3rd part = $$\frac{3}{6}$$ × 6000= 1000

Question 7.
Divide 17,640 a many P, Q, R and S such that O gets $$7^{\text {th }}5$$ of P, R gets $$5^{\text {th }}8$$ of Q and S gets $$\frac{2^{t h}}{13}$$ of the sum of Q and R.
Speed of Ragdhari express =$$=\frac{2880}{18}$$
Speed of Nilachala express = $$\frac{2880}{24}$$
Ratio of average speed = $$\frac{2880}{18}: \frac{2880}{24}$$ = 24:18 = 4:3