Chapter 10: Direct and Inverse Proportions

Q91Written answer

Match each of the entries in Column I with the appropriate entry in Column II.

Column I	Column II
1. x and y vary inversely to each other	$\dfrac{x}{y}$ = cons tan t
2. Mathematical representation of inverse variation of quantities p and q	y will increase in proportion
3. Mathematical representation of direct variation of quantities m and n	xy = Constant
4. When x = 5, y = 2.5 and when y = 5, x = 10	p $\alpha $ $\dfrac{1}{q}$
5. When x = 10 , y = 5 and when x = 20, y = 2.5	y will decrease in proportion
6. x and y vary directly with each other	x and y are directly proportional
7. If x and y vary inversely then on G. m α n decreasing x	m $\alpha $ n
8. If x and y vary directly then on decreasing x	x and y vary inversely
	p $\alpha $ q
	m $\alpha $ $\dfrac{1}{n}$

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Ans:

Column I	Column II
1. x and y vary inversely to each other	xy = constant
2. Mathematical representation of inverse variation of quantities p and q	p $\alpha $ $\dfrac{1}{q}$
3. Mathematical representation of direct variation of quantities m and n	m $\alpha $ n
4. When x = 5, y = 2.5 and when y = 5, x = 10	x and y are directly proportional
5. When x = 10 , y = 5 and when x = 20, y = 2.5	x and y vary inversely
6. x and y vary directly with each other	x and y are directly proportional
7. If x and y vary inversely then on G. m α n decreasing x	y will increase in proportion
8. If x and y vary directly then on decreasing x	y will decrease in proportion

Q92Written answer

There are 20 grams of protein in 75 grams of salted fish. How many grams of protein is in 225 gm of that fish?

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Ans: 75 gm fish holds protein = 20gm

1 gm of fish will hold = $\dfrac{20}{75}$

225 gm of fish will hold = $\dfrac{20}{75}\times $ 225=60gm

Q93Written answer

Ms. Anita has to drive from Jhareda to Ganwari. She measures a distance of 3.5 cm between these villages on the map. What is the actual distance between the villages if the map scale is 1 cm = 10 km?

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Ans: Distance between jhareda to ganwari in the map = 3.5cm

Given scale 1cm = 10km

So actual distance between the villages = 35×10=35 km

Q94Written answer

A water tank casts a shadow 21 m long. A tree of height 9.5 m casts a shadow 8 m long at the same time. The lengths of the shadows are directly proportional to their heights. Find the height of the tank.

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Ans: Height of the tree = 9.5cm

Shadow of the tree = 8cm

The shadows are directly proportional then

Q95Written answer

The table shows the time four elevators take to travel various distances. Find which elevator is fastest and which is slowest.

	Distance (m)	Time (sec.)
Elevator-A	435	29
Elevator-B	448	28
Elevator-C	130	10
Elevator-D	85	5

How much distance will be traveled by elevators B and C separately in 140 sec? Who traveled more and by how much?

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Ans: Distance covered by elevator A in 1 sec =$\dfrac{435}{29}$ =15m

Distance covered by elevator B in 1 sec=$\dfrac{448}{28}$ =16m

Distance covered by elevator C in 1 sec = $\dfrac{130}{10}$ =13m

Therefore, Elevator C is slowest.

Distance covered by elevator B in 140s = 140×16=2240m

Distance covered by elevator C in 140s= 140×13=1820m

Elevator B covers more distance than C = 2240-1820=420m

Q96Written answer

A volleyball court is in a rectangular shape and its dimensions are directly proportional to the dimensions of the swimming pool given below. Find the width of the pool.

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Ans: Length of the volleyball court = 18m

Breadth of volleyball court= 9m

Length of pool = 775m

Let’s assume length of the swimming pool = xm

$\dfrac{9}{18}$ = $\dfrac{x}{75}$

$\Rightarrow x$ = $\dfrac{75 \times 9}{18}$ = $\dfrac{75 }{2}$ = 37.5m

Q97Written answer

A recipe for a particular type of muffins requires 1 cup of milk and 1.5 cups of chocolates. Riya has 7.5 cups of chocolates. If she is using the recipe as a guide, how many cups of milk will she need to prepare muffins?

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Ans: Muffin requires 1 cup of milk and 1.5 cups of chocolates

Riya has 7.5 cups of chocolates

The number of cups of milk required for 7.5 cups of chocolate = $\dfrac{7.5}{1.5}$= 5cups

Q98Written answer

Pattern B consists of four tiles like pattern A. Write a proportion involving red dots and blue dots in pattern A and B. Are they in direct proportion? If yes, write the constant of proportion.

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Ans: No. Of red dots = 4

No. Of blue dots = 2

Pattern B consists of four tiles like pattern A

Pattern A×4=Pattern B

Proportion of pattern =$\dfrac{2}{6}$ = $\dfrac{1}{3}$

Proportion of red dots and blue dots in pattern B =$\dfrac{8}{32}$=$\dfrac{1}{4}$

Q99Written answer

A bowler throws a cricket ball at a speed of 120 km/h. How long does this ball take to travel a distance of 20 meters to reach the batsman?

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Ans: Speed of the cricket ball = 120km/hr = $\dfrac{120 \times 1000}{60}$ =2000m / min

Q100Written answer

The variable x is inversely proportional to y. If x increases by p%, then by what percent will y decrease?

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Ans: xy = k(constant)

The variable x is inversely proportional to y.

If an increase causes a decrease in y and vice-a-versa this is called the inverse proportion.

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