A and B started a business in partnership investing Rs 20000 and Rs 15000 respectively After six months C joined them with Rs 20000 what will be Bs share in the total profit of Rs 25000 earned at the end of two years from the starting of the business

HARD

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

The cost of milk per litre is $₹ 15$ . Draw the graph for the relation between the quantity and cost. Hence find the proportionality constant.

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A certain sum is divided among A, B and C in such way that A gets Rs.

40

more than half of the sum. B gets Rs.

120

less than three-eighths of the sum and C gets Rs.

200

. What is the total sum?

HARD

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

The cost of milk per litre is $₹ 15$ . Draw the graph for the relation between the quantity and cost. Hence find the cost of $3$ litres of milk..

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

If $p$ persons working $p$ hours a day for each of $p$ days produce $p$ units of work, then the units of the work produced by $q$ persons working $q$ hours a day for each $q$ day is:

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Pihu and Rani started a business together by investing

₹ 9000

and

₹ 6300

respectively. After a certain period, Pihu withdrew from the business completely. If at the end of two years, the total profit earned was

₹ 13050

and Pihu's share was

₹ 6750

, after how many months did Pihu withdrew from business?

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

How much time the minute hand of a clock will take to describe an angle of

\frac{2 π}{3}

radians ?

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A car consumes

5.4 litres

of petrol to cover

60.48 km

, how many kilometres be covered with

22 litres

of petrol?

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A sum of

₹ 549

is to be divided among Priya, Preeti and Sonu in such a way that

3

times Priya's share,

4

times Preeti's share and

7

times Sonu's share are all equal. What is the share of Priya?

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A and B started a business with initial investments in the ratio

5 : 7

. If, after one year their profits were in the ratio

1 : 2

and the period for A's investment was for

7

months only, B invested the money for how many months?

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A, B

and

C

started a business with their investment in the ratio

1 : 3 : 5

. After

4

months,

A

invested the same amount as before and

B

as well as

C

withdrew half of their investments. What is the ratio of their profits at the end of the year?

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A set of farmers can completely harvest a crop in

10

days. However

12

farmers fell ill and now the remaining can do this job in

15

days. Find the original number of farmers.

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A started $y$ business. After

4

months from the start of the business, B and C joined. The respective ratio between the investments of A, B and C was

4 : 6 : 5

. If A's share in annual profit was Rs.

250

more than C's share, what was the total annual profit earned?

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

If

x

varies as

y z

, then

y

varies inversely as

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

If

x α y

then

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Mayank can do a piece of work in

3

days. Sanjay can do the same work in

4

days. The wage for full work is

₹ 350

. If both work together to complete the work, then find out the earning of Sanjay if the wages are paid in proportion to work done.

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A vessel contained a solution of acid and water in which water was

64 %

. Four litres of the solution were taken out of the vessel and the same quantity of water was added. If the resulting solution contains

30 %

acid, the quantity(in litres) of the solution, in the beginning in the vessel, was

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

If

y = 3 + 1.9 x

, and mode of

x

is

15

, then the mode of

y

is:

HARD

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

There are two candles of same length and same size. Both of them burn at uniform rate. The first, one burns in

5

hours and the second one burns in

3

hours. Both the candles are lit together. After how many minutes the length of the first candle is

3

times that of the other?

MEDIUM

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

A and B both starts a business. Amount invested by B is one-third of that invested by A. Three months from the start of the business, A withdrew one-third of his investment and B tripled his investments. If from the total annual profit earned, A receives Rs.

1800

as his share from the profit, what was the total annual profit earned?

EASY

Mathematics>Arithmetic>Ratios and Proportional Relationships>Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Gita, Shweta and Sita invested

Rs . 4200

,

Rs . 8400

and

Rs . 5400

respectively while starting a business. At the end of the year, they earned a profit of

Rs . 24, 000

. Sita invested

32 %

of her share of the profit in a savings scheme. How much amount is left with her?

A and B started a business in partnership investing Rs. 20,000/- and Rs. 15,000/- respectively. After six months 'C' joined them with Rs. 20,000/- what will be B's share in the total profit of Rs. 25,000/- earned at the end of two years from the starting of the business?

Important Questions on Ratios and Proportional Relationships

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