# Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 2 Life Mathematics Intext Questions

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## Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 2 Life Mathematics Intext Questions

Exercise 2.1
Try These (Text book Page No. 33)

Classify the given examples as direct or inverse proportion:
(i) Weight of pulses to their cost.
Solution:
As weight increases cost also increases.
∴ Weight and cost are direct proportion.

(ii) Distance travelled by bus to the price of ticket.
Solution:
As the distance increases price to travel also increases.
∴ Distance and price are direct proportion.

(iii) Speed of the athelete to cover a certain distance.
Solution:
As the speed increases, the time to cover the distance become less.
So speed and time are in indirect proportion.

(iv) Number of workers employed to complete a construction in a specified time.
Solution:
As the number of workers increases, the amount of work become less, so they are in indirect proportion.

(v) Volume of water flown through a pipe to its pressure.
Solution:
As the pressure increases, volume also increases.
∴ They are direct proportions.

(vi) Area of a circle to its radius.
Solution:
If the radius of the circle increases its area also increases.
∴ Area and radius of circles are direct proportion.

Use the concept of direct and inverse proportions and try to answer the following questions:
Question 1.
A student can type 21 pages in 15 minutes. At the same rate, how long will it take the student to type 84 pages?
Solution:
Direct proportion
No. of minutes = x
k = $$\frac{21}{15}$$
$$\frac{21}{15}$$ = $$\frac{84}{x}$$

Question 2.
The weight of an iron pipe varies directly with its length. If 8 feet of an iron pipe weighs 3.2 kg, find the proportionality constant k and determine the weight of a 36 feet iron pipe.
Solution:

Weight of 36 feet iron pipe = x
$$\frac{36}{x}$$ = 2.5

Question 3.
A car covers a distance of 765 km in 51 litres of petrol. How much distance would it cover in 30 litres of petrol?
Solution:
Direct proportion
k = $$\frac{51}{765}$$
Distance cover = x km
$$\frac{30}{x}$$ = $$\frac{51}{765}$$

Question 4.
If x and y vary inversely and x = 24 when y = 8, find x when y = 12.
Solution:
k = xy = 24 × 8 = 192
∴ 12 × x = 192

Question 5.
If 35 women can do a piece of work in 16 days, in how many days will 28 women do the same work?
Solution:
Inverse proportion
No. of days = x
k = 35 × 16
∴ 28 × x = 35 × 16

Question 6.
A farmer has food for 14 cows which can last for 39 days. How long would the food last, if 7 more cows join his cattle?
Solution:
Inverse variation
k = xy = 14 × 39
No. of cow = 14 + 7 = 21
No. of days = x
21 × x = 14 × 39

Question 7.
Identify the type of proportion and fill in the blank boxes:

Solution:
Direct proportion
$$\frac{x}{y}$$ = k = $$\frac{1}{20}$$
(i) x = 2; y = ?
$$\frac{2}{y}$$ = $$\frac{1}{20}$$ ⇒ y = 2 × 20 = 40

(ii) x = ?; y = 60
$$\frac{x}{60}$$ = $$\frac{1}{20}$$ ⇒ x = $$\frac{60}{20}$$ = 3

(iii) x = 4; y = ?
$$\frac{4}{y}$$ = $$\frac{1}{20}$$ ⇒ y = 80

(iv) x = 4; y = ?
$$\frac{8}{y}$$ = $$\frac{1}{20}$$ ⇒ y = 20 × 8 = 160

(v) x = ?; y = 180
$$\frac{x}{180}$$ = $$\frac{1}{20}$$
x = $$\frac{180}{20}$$ = 9

(vi) x = 12; y = ?
$$\frac{12}{y}$$ = $$\frac{1}{20}$$
y = 12 × 20 = 240

(vii) x = ?; y = 360
$$\frac{x}{360}$$ = $$\frac{1}{20}$$ ⇒ x = $$\frac{360}{20}$$ = 18

(viii) x = 24; y = ?
$$\frac{24}{y}$$ = $$\frac{1}{20}$$ ⇒ y = 24 × 20 = 480

Question 8.
Identify the type of proportion and fill in the blank boxes:

Solution:
Inverse proportion
k = xy = 1 × 144 = 144
(i) x = 2; y = ?
2y = 144
y = 72

(ii) X = ?; y = 48
48x = 144
x = $$\frac{144}{48}$$ = 3

(iii) x = 4; y = ?
4y = 144
y = $$\frac{144}{4}$$ = 36

(iv) x = 8; y = ?
8 y = 144
y = $$\frac{144}{8}$$ = 18

(v) x = ?; y = 16
16x = 144
y = $$\frac{144}{16}$$ = 9

(vi) x = 12; y = ?
12y = 144
y = $$\frac{144}{12}$$ = 12

(vii) x = ?; y = 9
9x = 144
x = $$\frac{144}{9}$$ = 16

(viii) x = 24; y = ?
24y = 144
y = $$\frac{144}{24}$$ = 6

Try These (Text book Page No. 38)

Question 1.
When x = 5 and y = 5 find k, if x and y vary directly.
Solution:
If x and y vary directly then $$\frac{x}{y}$$ = k
Here x = 5; y = 5
∴ k = $$\frac{5}{5}$$
k = 1

Question 2.
When x and y vary inversely, find the constant of variation when x = 64 and y = 0.75
Solution:
Given
x =64, y = 0.75
and also given x and y vary inversely.
∴ xy = k. the constant of variation.
∴ Constant = 64 × 0.75
Constant of variation = 48

Think (Text book Page No. 38)

(i) When x and y are in direct proportion and if y is doubled, then what happens to x?
Solution:
If x and y are in direct proportion $$\frac{x}{y}$$ = k, constant.
if y is doubled, then $$\frac{x}{2}$$ must be equal to k. So x also to be doubled.

(ii) if $$\frac{x}{y-x}$$ = $$\frac{6}{7}$$ What is $$\frac{x}{y}$$?
Solution:
if $$\frac{x}{y-x}$$ = $$\frac{6}{7}$$
$$\frac{y-x}{x}$$ = $$\frac{7}{6}$$
$$\frac{y}{x}$$ – $$\frac{x}{x}$$ = $$\frac{7}{6}$$
$$\frac{y}{x}$$ = $$\frac{7}{6}$$ + $$\frac{x}{x}$$
$$\frac{y}{x}$$ = $$\frac{7}{6}$$ + 1
$$\frac{y}{x}$$ = $$\frac{7+6}{6}$$
$$\frac{y}{x}$$ = $$\frac{13}{6}$$
$$\frac{x}{y}$$ = $$\frac{6}{13}$$

Try These (Text book Page No. 40)

Identify the different variations present in the following questions:
Question 1.
24 men can make 48 articles in 12 days. Then, 6 men can make …………. articles in 6 days.
Solution:
Let the required no. of articles be x

(i) Mens and days are Indirect variables.
(ii) Men and Articles are direct variables
(iii) Days and articles are also direct variables using formula.
Let P1 = 24, D1 = 12, W1 = 48
P2 = 6, D2 = 6, W2 = x

Question 2.
15 workers can lay a road of length 4 km In 4 hours. Then, …………. workers can lay a road of length 8 km in 8 hours.
Solution:
Let the required number of workers be x

Length and workers are direct variable as more length need more workers.
The proportion is 4 : 8 : : 15 : x ……….(1)
Hours and workers are indirect variables as more working hours need less men.
∴ The proportion is 8 : 4 : : 15 : x ………..(2)
Combining (1) and (2)

Product of the extremes = product of the means
4 × 8 × x = 8 × 4 × 15
x = $$\frac{8×4×15}{4×8}$$
x = 15 workers

Question 3.
25 women working 12 hours a day can complete a work in 36 days. Then, 20 women must ……….. work hours to complete the same work in 30 days.
Solution:
Let the required hours be x

As women increases hours to work decreases
∴ It is an inverse proportion.
∴ Multiplying factor is $$\frac{25}{20}$$
As days increases hours needed become less
∴ It is also an indirect variation.
∴ Multiplying factor is $$\frac{36}{30}$$
∴ x = 12 × $$\frac{25}{20}$$ × $$\frac{36}{30}$$
x = 18 hours

Question 4.
In a camp, there are 420 kg of rice sufficient for 98 persons for 45 days. The number of days that 60 kg of rice will last for 42 persons is…………
Solution:
Let the required number of days be x.

If amount of rice is more it will last for more days.
∴ It is Direct Proportion.
∴ Multiplying factor is $$\frac{60}{420}$$
If men increases number of days the rice lasts decreases
∴ It is an inverse proportion.
∴ Multiplying factor is $$\frac{98}{42}$$
x = 45 × $$\frac{60}{420}$$ × $$\frac{98}{42}$$

x = 15 days

Try These (Text book Page No. 44)

Question 1.
Vikram can do one-third of work in p days. He can do $$\frac{3}{4}$$th of work in ………… days.
Solution:
$$\frac{1}{3}$$ of the work will be done in p days
∴ Full work will be completed in 3p days
$$\frac{3}{4}$$th of the work will be done in = 3p × $$\frac{3}{4}$$ = $$\frac{9}{4}$$p = 2$$\frac{1}{4}$$p days

Question 2.
If m persons can complete a work in n days, then 4m persons can complete the same work in ……….. days and $$\frac{m}{4}$$ persons can complete the same work in…….. days
Solution:
Given m persons complete a work in n days
(i) Then work measured in terms of Man days = mn
4 m men do the work it will be completed in $$\frac{mn}{4m}$$ days = $$\frac{n}{4}$$ days.
(ii) $$\frac{m}{4}$$ persons can complete the same work in $$\frac{mn}{\frac{m}{4}}$$ days = $$\frac{4mn}{m}$$ = 4n days