EASY

Earn 100

The sum of three consecutive integers is $78$ . Find the numbers.

Important Questions on Linear Equations in Two Variables

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

x, y, z

are three integers such that

x + y = 8

y + z = 13

and

z + x = 17

, then the value of

\frac{x^{2}}{y z}

is:

HARD

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

3

chairs and

2

tables cost

R s . 700

and

5

chairs and

3

tables cost

R s . 1100

. What is the cost of

1

chair and

2

tables?

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

4

5^{t h s}

of an estate is worth Rs. 16800, then the value of

3

7^{t h s}

of the estate is

HARD

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Positive integers

x, y, z

satisfy

x y + z = 160

. Compute the smallest possible value of

x + y z

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

The population of Patna city is $96000$ , the decreasing rate of population is $800$ per year. Population of Patliputra is $68000$ , the increasing rate of population is $1200$ per year. In how many years will the population of both places be equal?

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

A sum of

₹ 8, 200

was divided among

A, B

and

C

in such a way that

A

had

₹ 500

more than

B

and

C

had

₹ 300

more than

A

. How much was

C' s

share (in

₹

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

A number exceeds its

\frac{1}{9}

64

. What is the number?

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Fifty litres of a mixture of milk and water contains

30

percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains

20

percent of water. Then, how many litres of water should be added th the resulting mixture to obtain a final mixture that contains

25

percent of water?

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Find the value of

x

after solving the following equation.

0.12 \times (5 x - 4) = 0.5 x + 0.8

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Find the value/values of x for the given equation.

$2^{(2 x + 3)} - 17 = 9 (2^{x} - 2)$

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

A book is published in three volumes, the pages being numbered from

1

onwards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is

50

more than that in the first volume, and the number pages in the third volume is one and a half times that in the second. The sum of the page numbers on the first pages of the three volumes is

1709 .

n

is the last page number, what is the largest prime factor of

n

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

P and Q are two examination halls. If

10

examinees are sent from P into Q, the number of examinees becomes equal in both the halls. If

20

examinees are transferred from Q into P, the number of examinees becomes double in P in comparison with Q. What is the number of examinees in each P and Q separately ?

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

x

and

y

are positive integers such that

(x - 4) (x - 10) = 2^{y}

, find the maximum possible value of

(x + y)

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

While tabulation of marks scored in an examination by the students of a class, by mistake the marks scored by one student got recorded as

93

in place of

63

, and thereby the average marks increased by

0.5

. What was the number of students in the class?

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

X and Y

together have

₹ 1300

. If

₹ 10

less than three-fifth of the amount

X

is equal to half of the amount

Y

, then how much does

X

have?

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

In equation

3 x + 2 y = 7

, if

y = 2

then, write the value of

x

HARD

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Three workers working together need

1

hour to construct a wall. The first worker, working alone, can construct the wall twice as fast at the third worker, and can complete the task an hour sooner than the second worker. Then, the average time in hours taken by the three workers, when working alone, to construct the wall is

HARD

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

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

10

. When the digits are reversed, the number decreases by

54

. Find the changed number:

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

x

and

y

are positive integers and

\frac{3 x}{y} = 4,

then find the minimum value of

(3 x + 4 y)

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

A number of two digits is equal to '

k

' times to the sum of these digits. If the places of these digits are mutually exchanged. the newly formed number is equal to the sum of these digits multiplied by which one of the following options ?

The sum of three consecutive integers is 78. Find the numbers.

Important Questions on Linear Equations in Two Variables

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The sum of three consecutive integers is $78$ . Find the numbers.