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Test: Equations Reducible to Linear Form - CAT MCQ


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20 Questions MCQ Test Additional Study Material for CAT - Test: Equations Reducible to Linear Form

Test: Equations Reducible to Linear Form for CAT 2024 is part of Additional Study Material for CAT preparation. The Test: Equations Reducible to Linear Form questions and answers have been prepared according to the CAT exam syllabus.The Test: Equations Reducible to Linear Form MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Equations Reducible to Linear Form below.
Solutions of Test: Equations Reducible to Linear Form questions in English are available as part of our Additional Study Material for CAT for CAT & Test: Equations Reducible to Linear Form solutions in Hindi for Additional Study Material for CAT course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt Test: Equations Reducible to Linear Form | 20 questions in 20 minutes | Mock test for CAT preparation | Free important questions MCQ to study Additional Study Material for CAT for CAT Exam | Download free PDF with solutions
Test: Equations Reducible to Linear Form - Question 1
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The value of x, y in the following pair of Linear equations is:  , 

Test: Equations Reducible to Linear Form - Question 2
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The value of x, y in the following pair of Linear equations is:  , 

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Test: Equations Reducible to Linear Form - Question 3
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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.

Detailed Solution for Test: Equations Reducible to Linear Form - Question 3

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

Test: Equations Reducible to Linear Form - Question 4
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The value of x, y in the following pair of Linear equations is:  , 
Test: Equations Reducible to Linear Form - Question 5
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The value ofx,y in the following pair of Linear equations is:,  
Detailed Solution for Test: Equations Reducible to Linear Form - Question 5
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
Test: Equations Reducible to Linear Form - Question 6
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The value of x, y in the following 2x + 2 – 3y + 1 = 5 ………(1) , 2x + 3y = 17 ………(2)​
Test: Equations Reducible to Linear Form - Question 7
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The value of x, y in the following pair of Linear equations is: 

  ​
Test: Equations Reducible to Linear Form - Question 8
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The value of x, y in the following pair of Linear equations is: , 
Test: Equations Reducible to Linear Form - Question 9
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The value ofx, y in the following pair of Linear equations is:
Test: Equations Reducible to Linear Form - Question 10
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If 6x + 3y = 6xy; 2x + 4y = 5xy, then the values of x and y are​
Test: Equations Reducible to Linear Form - Question 11
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The values of x and y , if  
Test: Equations Reducible to Linear Form - Question 12
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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
Test: Equations Reducible to Linear Form - Question 13
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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?​
Test: Equations Reducible to Linear Form - Question 14
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The value of x, y in the following pair of Linear equations is: , 
Where  x + y ≠ 0 and x - y ≠ 0 ?
Test: Equations Reducible to Linear Form - Question 15
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The solution of the following pair of Linear equations is: 

 ​
Test: Equations Reducible to Linear Form - Question 16
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Find x and y given  , ​
Test: Equations Reducible to Linear Form - Question 17
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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​
Test: Equations Reducible to Linear Form - Question 18
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The values of x and y that satisfy the pair of equations: 
​
Test: Equations Reducible to Linear Form - Question 19
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If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y are​
Test: Equations Reducible to Linear Form - Question 20
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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?
Detailed Solution for Test: Equations Reducible to Linear Form - Question 20

CP = 405 / 0.9 = 450
New SP = Rs. 465
Profit (%) = [465-450 / 450] X 100 = 3.33%

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