Samacheer Class 7 Maths - Direct and Inverse Proportion Intext Questions

(i) 1 kg = 1000 g
∴ 5 kg = 5000 g
∴ 555 g : 5 kg = 555 g : 5000 g = 111 : 1000
(ii) 21 km to 175m
1 km = 1000 m
21 km = 21 × 1000 = 21,000m
∴ 21 km : 175 m = 21000 : 175 = 120 : 1

(i) Given 110 : x :: 8 : 88
Product of the means = Product of the extremes
x × 8 = 110 × 88(ii) x : 26 :: 5 : 65
Product of the means = Product of the extremesTry this (Text Book Page No. 74)

Let the number of students be x and the number of chocolates be y. As the valve of x increases also correspondingly increases.
ie \(\frac{x}{y}=k\)
∴ x and y are in direct proportion.
Try This (Text book Page No. 74)

Perimeter of the square y = 4x, units where x is the side of a squareCompleting the tableFrom the above table we find that as x increases y also increased in such a way that \(\frac{x}{y}=\frac{1}{4}\), constant.
∴ Side of a square is in direct proportion to the perimeter of the square.
Try this (Text book Page No. 75)

Some other examples of such kind are
(i) Cost of book and number of books
(ii) Distance and time to travel
(iii) Men workers and wages.
Exercise 4.2
Try this (Text book Page No. 78)

Let the required number of students be x.As the number of students increases the entry fees also increases.
∴ They are in direct proportion .∴ The number of students entered magic show = 42

Let the number of people attended the party be x.As the number of trips increases, number of people also increases.
∴ They are in direct proportion.180 people attend the party in 12 trips

Let the required height of the pole be ‘x’ m.Height of the pole and its shadow are in direct proportion∴ Height of the pole x = 40m.

Weight of 72 books = 9 kg = 9000 g
∴ Weight of 1 book = \(\frac{9000}{72}\) = 125 g
∴ Weight of 40 books = 125 × 40 g = 5000 g = 5 kg.
Weight of 40 books = 5 kg

Rent paid by Thamarai for 3 months = ₹ 7500
∴ Rent paid for 1 month = \(\frac{7500}{3}\) = 2500
Rent paid for 1 year or 12 moths = 2500 × 12 = ₹ 30,000
For 1 year rent to be paid = ₹ 30,000

Let the required number of days be x.As the number of ducks decreases the food will last for more days.
∴ They are in inverse proportion. x 1 y 1 = x 2 y 2The food lasts for 36 days

Let the number of days required be x.As the number of machines increases it takes less days to complete the work
∴ They are in inverse proportion, x 1 y 1 = x 2 y 2It takes 20 days to dig the hole

Let the required number of days be x.As the number of students increases the food last for less number of days
∴ They are in inverse proportion.The food stock lasts for 15 days

Let the required weight of the parcel be x grams.As the number of parcels increases weight of a parcel decreases.
∴ They are in inverse proportion.Weight of each parcel = 100 grams

Let the, number of gardeners needed be x.As the number of gardeners increases the time decreases. They are in inverse proportion,
x 1 y 1 = x 2 y 2∴ To complete the work in 30 min gardeners needed = 24
Already existing gardeners = 6
∴ More gardeners needed = 24 – 6 = 18
18 more gardeners are needed

Let the speed to reach school in 15 min be x∴ They are in inverse proportion x 1 y 1 = x 2 y 2If she reaches in 15 min the speed = 16 km/hr
Already running with 12 km / hr
∴ Increased speed = 16 – 12 = 4km / hr
Increase in speed = 4 km / hr

Let the required number of machines be xAs the number of machines increases number of days required decreases.∴ 24 machines would be required
Objective Type Questions

(i) For ₹ 84 weight of onion bought
for ₹ 1 weight of onion bought
∴ For ₹ 180 weight of onion bought w
∴ For ₹ 180 weight of onion bought
(ii) Cost of 7 kg of onions = 15 kg

Let the number of years required be x.No. of years and deposit are direct proportion as they both increases simultaneously.He can save ₹ 1,50,000 in \(7 \frac{1}{2}\) years.

Let the required time taken to print be x
As the speed increases time taken to print decreases
∴ They are in inverse proportion
Time taken to print 30 pages = 1 min

Let the cost required be xAs number of cans increases cost also increases.
∴ They are in direct proportionx = 140
Cost of 4 cans of juice = 140

Let the required distance be xAs the distance increases fuel quantity also increases.
∴ They are direct proportion.∴ The diesel required = 300 liters
Challenge Problems

Let the required number of days if 14 farmers ploughed = xAs number of farmers increases, number of days decreases.
∴ They are in inverse proportionInitially the farmers worked for 21 days. Now they worked for 15 days.
∴ The number of days reduced = 21 – 15 = 6 days

As number of people increases food last for less number of days.Remaining food is to be used for 50 days.
But it only last for 40 days.
No. of days shortage = 50 – 40 = 10 days.
∴ 10 days of food shortage due to the addition of 20 more people.

As the number of men increases number of days increases.
∴ They are inversely proportionalx = 5 days
∴ Remaining work will be complete in 5 days
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