Three liner equation problems for practice

Question 1
Green and blue coloured toys are 149 in number in a box. Two green toys are removed from the lot and now there are twice as many green ones as blue ones. How many green coloured toys are there now?
a) 76 b) 86 c) 90 d) 98
Answer : d) 98
Solution:
Let x and y be the original number of green and blue toys respectively. Originally there were 149 toys. Hence,
x + y = 149 ----------(1)
After two green toys were removed, the number of green toys becomes twice that of the blue toys.
x-2 = 2 y -----------(2)
Solving eq 1 and eq 2 we get
3 y = 149-2=147
y= 49
Current number of green toys (after removal of two) is twice as that of blue ones.So the green toys are 98 in number.
Question 2
Roushan was a B.E student pursuing studies in the city of Vizag. During summer holidays he visited his village.In the courtyard of his house, there are many hens and goats. Roushan asked his sister as to how many hens are there in the courtyard. His sister who is a village girl gave her reply like this : If you count all the heads you will get 300. But if you count the legs you will get 700. Can you help Roushan in calculating the number of hens.
(a) 200 (b) 250 (c) 600 (d) 400
Answer : b) 250
Solution:
Let us assume that x number of hens and y number of goats are there in the courtyard.
x+y = 300, -------(1) since the total head count is given as 300.
Its given, there are totally 700 legs when counted. We know the hens have two legs and the goats have 4 legs. Therefore
2x+4y= 700 -------(2)
(1)x2 will give, 2x+2y=600 -------(3)
(2)-(3) will give you, 2y=100 and y=50.
Substituting in equation (1) you get x value as 250
Question 3
Average age of three brothers is 5. Youngest brother thinks, "If I had born earlier along with the middle brother, I would be just short of 8 years compared to my eldest brother". Middle brother thinks, "If I had born later along with my younger brother, I would be short of 10 years compared to my eldest brother." What is the age of middle brother ?
a) 3 years b) 1 year c) 2 years d) 4 years
Answer : a) 3 years.
Solution :
Let x,y and z be the ages of youngest, middle and eldest brother.
The average of their ages is 5. i,e x + y + z / 3 = 5 Or x + y + z = 15 ...(1)
Youngest brother thinks that If he had born earlier along with his middle brother he would be just short of 8 years compared to his eldest brother.
This statement implies that if youngest brother had the age of his middle brother he would be short of 8 years compared to his eldest brother. This indirectly implies that middle brother is short of eldest brother by 8 years.
i.e z - y = 8 ...(2)
Similarly the middle brother thinks if he was as old as his youngest brother he would be short of 10 years compared to his eldest brother. This indirectly implies that youngest brother is 10 years lesser than eldest brother.
i.e z - x = 10 ...(3)
Adding equations 1,2 and 3, we get
3z = 33 or z = 11
Substitute z = 11 in eq 2 we get,
11 - y = 8
Or y = 3
Therefore age of middle brother is 3 years.

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10th 3i InfoTech Academic Books Accenture ACIO ActiveX ADT Agricultural AIEEE Air Force Algebraic Amdocs Android Answers Application Development Aptitude Aptitude Questions Architectures ASP ATOS B.Sc B.Tech.B.E. Bank Exam BCA BE Board Exam Books break-continue Business Plan C C Programming C# C++ Campus campus interview Candidate profile Capgemini Career CDS Certification CET Challenge Circle Cisco class code Cognizant communication Company Company Profile Competitive Exams computer Computer Networks concentric circles constructor Course Credit Suisse CSS CTS Data Structure DBMS DC Deloitte difficult interview questions dimensions Distributed Computing do while dotNet Download ds Dynamic Web Development e-Admit card Educational engineering entertainment Even Odd Events exam schedule exception for loop fresher GATE general Discussion general knowledge Get Placed Government Job Hall Ticket HCL how to answer How to Prepare HR HR Interview HSC hypertext preprocessor IB IBM IBPS IIT Indian Army Information infosys Intelligence Bureau Internship interview Experience interview questions Interview Tips IntroC IntroC# IntroJava IntroPHP IT J2EE J2ME Java JavaScript jobs Language Books Language Tutorial Languages limit number of objectsJava Limit the number of objects being created in JAVA Linux Linux Administrator Linux Developer Logical Questions loops M Tech M.E. M.Tech M.Tech AND B.Tech Management Management Skills Matrices MBA mca ME microsoft mistakes Mixture Mobile Computing mock questions mock test MySql naukri NDA OOP opening Operating System Oracle paper Persistent PHP php programming php string variables PL/SQL Placement placement guide Placement Paper Placement Process preparing for placement presentation probability Problems Professional program Programming Project Engineer project idea Projects Puzzle qualities Question of the day Questions Quiz Question Recruitment Recruitment Pattern Requirement Result Resume Reviews Screen Sizes Scripting Session Skills Software Software Engineering solved papers Source Code Speed time and distance SQL SSC story Stress Interview Study Material study tips submit resume Synonym TCS Tech Mahindra tech news Technical Books Technical Interview Testing thank you letter Thought Time Table TutC++ Unix questions asked in aptitude and inteviews for MCA UPSC verbal Web Designing Web Developer Website Development What to read while loop Wipro Writing Resume