The distance travelled in t seconds by an object starting with a speed of u metres/second and moving along a straight line with speed increasing at the rate of a metres/second every second is given by u t + 1 2 a t 2 metres. An object moving in this manner travels 10 metres in 2 seconds and 28 metres in 4 seconds. With what speed did it start? At what rate does its speed change?

Given that the distance traveled is d = u t + 1 2 a t 2 . When t = 2 s , d = 10 m . Putting these values in the formula, we get, 10 = u × 2 + 1 2 a × 2 2 ⇒ u + a = 5 -----(i) Also, given that when t = 4 s , d = 28 m . Also, putting those values in the formula, we obtain, 28 = u × 4 + 1 2 a × 4 2 ⇒ 28 = 4 u + 8 a ⇒ u + 2 a = 7 ......(ii) Subtracting equation (i) and (ii), we get, a = 2 Substituting a = 2 in equation (ii), we get ⇒ 5 + a = 7 [replace the value of u + a from (i)] ⇒ a = 7 - 5 = 2 Putting the value of a in (i), we get, u + 2 = 5 ⇒ u = 5 - 2 = 3 Therefore, the starting speed of the object is 3 m / s and the rate of the change of speed is 2 m / s / s .

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9th Kerala Board

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A man invested $10000$ rupees, split into two schemes, at annual rates of interest $8 %$ and $9 % .$ After one year he got $875$ rupees as interest from both. How much did he invest in each?

Important Questions on Pairs of Equations

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9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 1>Q (4)

A three and a half metre long rod is to be cut into two pieces, one piece is to be bent into a square and the other into an equilateral triangle. The length of their sides must be the same. How should it be cut?

HARD

9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 1>Q (5)

The distance travelled in

t

seconds by an object starting with a speed of

u

metres/second and moving along a straight line with speed
increasing at the rate of

a

metres/second every second is given by

u t + \frac{1}{2} a t^{2}

metres. An object moving in this manner travels

10

metres in

2

seconds and

28

metres in

4

seconds. With what speed did it start? At what rate does its speed change?

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9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 2>Q (1)

Raju bought seven notebooks of two hundred pages and five of hundred pages, for

107

rupees. Joseph bought five notebooks of two hundred pages and seven of hundred pages, for

97

rupees. What is the price of each kind of notebook?

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9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 2>Q (2)

Four times a number and three times another number added together make

43

. Two times the second number, subtracted from three times the first gives

11

. What are the numbers?

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9th Kerala Board

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Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 2>Q (3)

The sum of the digits of a two-digit number is

11

. The number got by interchanging the digits is

27

more than the original number. What is the number?

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9th Kerala Board

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Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 2>Q (4)

Four years ago, Rahim's age was three times Ramu's age. After two years, it would just be double. What are their ages now?

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9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 2>Q (5)

If the length of a rectangle is increased by

5

metres and the breadth decreased by

3

metres, the area would decrease by

5

square metres. If the length is increased by

3

metres and breadth increased by

2

metres, the area would increase by

50

square metres. What are the length and breadth?

HARD

9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 3 - Pairs of Equations>Exercise 3>Q (1)

10

metre long rope is to be cut into two pieces and a square is to be made using each. The difference in the areas enclosed must be

1 \frac{1}{4}

square metres. How should it be cut?

A man invested 10000 rupees, split into two schemes, at annual rates of interest 8% and 9%. After one year he got 875 rupees as interest from both. How much did he invest in each?

Important Questions on Pairs of Equations

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A man invested $10000$ rupees, split into two schemes, at annual rates of interest $8 %$ and $9 % .$ After one year he got $875$ rupees as interest from both. How much did he invest in each?