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QUESTION: 1

The value of x, y in the following pair of Linear equations is: ,

Solution:

QUESTION: 2

The value of x, y in the following pair of Linear equations is: ,

Solution:

QUESTION: 3

The sum of ages of A and B is 49 years. A said to B, “I am twice as old as you were when I was as old as you are. Find the present age of B.

Solution:

Let the ages of A and B be a and b

Going by the statement step by step

A says “I am twice as old”=A says that age is twice some number which is a=2( _ )

"as you were" which talks about past, means B’s age some times ago...which is b-(how many years ago)

So, a=2(b- (how many years ago))

“when I was as old as you are" = when A was B’s age now= When A was b years old. So no. of years from now to back then will be A’s age now minus A’s age then =a-b

a=2(b-(a-b))

a=4b-2a

a=4b/3 …..1

Also a+b=49

a=49-b …..2

From 1 and 2

49-b=4b/3

4b/3+b=49

7b/3=49

b=49*3/7=21 years

a=28 years

QUESTION: 4

The value of x, y in the following pair of Linear equations is: ,

Solution:

QUESTION: 5

The value ofx,y in the following pair of Linear equations is:,

Solution:
Firstly, let 1/√x= a and 1/√y=b

=> 2a+3b=2 -(1)

=> 4a-9b= -1 -(2)

Now, adding 3 times if equation (1) with equation (2)

=> 6a+9b=6

4a-9b=-1

=> 10a=5

=> a=1/2

Now, Subsituting the value of a in equation (1)

2(1/2) +3b=2

1+3b=2

3b=2-1

b=-1/3

Now, as a=1/√x and b=1/√y

1/√x= 1/2 and 1/√y=1/3

=> √x=2 and √y=3

Squaring both sides

=> x=4 and y=9

QUESTION: 6

The value of x, y in the following 2^{x + 2} – 3^{y + 1} = 5 ………(1) , 2^{x} + 3^{y} = 17 ………(2)

Solution:

QUESTION: 7

The value of x, y in the following pair of Linear equations is:

Solution:

QUESTION: 8

The value of x, y in the following pair of Linear equations is: ,

Solution:

QUESTION: 9

The value ofx, y in the following pair of Linear equations is:

Solution:

QUESTION: 10

If 6x + 3y = 6xy; 2x + 4y = 5xy, then the values of x and y are

Solution:

QUESTION: 11

The values of x and y , if

Solution:

QUESTION: 12

A boat goes 35 km upstream and 42 km downstream in 11 hours. In 14 hours, it can go 43 km upstream and 59 km down-stream. To determine the speed of the stream and that of the boat in still water , express the information in the form of equations of the type ax + by + c = 0

Solution:

QUESTION: 13

In an examination, one mark is awarded for every correct answer, while 1/4 mark is deducted for every wrong answer. A student answered 120 questions and got 20 marks. Which of the following pair of equations would give the result for how many questions did he answered correctly?

Solution:

QUESTION: 14

The value of x, y in the following pair of Linear equations is: ,

Where x + y ≠ 0 and x - y ≠ 0 ?

Solution:

QUESTION: 15

The solution of the following pair of Linear equations is:

Solution:

QUESTION: 16

Find x and y given ,

Solution:

QUESTION: 17

3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically are

Solution:

QUESTION: 18

The values of x and y that satisfy the pair of equations:

Solution:

QUESTION: 19

If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y are

Solution:

QUESTION: 20

By selling a wrist watch of Rs.405 the shopkeeper incurs a loss of 10%. What is the gain or loss percentage if he sells the same watch at Rs. 465?

Solution:

CP = 405 / 0.9 = 450

New SP = Rs. 465

Profit (%) = [465-450 / 450] X 100 = 3.33%

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