LearnPick Navigation

Answers and Solutions

What's Your Question?
Question: A vessel contain 60 litre of milk, 6 litre of milk is taken out and 6 litre of water is added to the vessel. Again 6 litre of milk is taken out and 6 litre of water is added to the vessel. What is the ratio of milk and water in the resulting mixture in the vessel.

Posted by: Bikas S. on 04.12.2020

Ask a Question
The ratio of milk to water is 4:1 Initially 60 litres of milk Take away 6 litres =54 litres Take away 6 litres = 48 litres Now 6+6 litres of water is added=12 Therefore 48:12 4:1

If a mixture having x unit of liquid and if y unit of liquid is taken out and filled with y unit of another liquid.Than after n iteration [x(1-y/x)^n] unit of original liquid will remain.

x = 60

y = 6

n = 2

Milk = 60[(1-6/60)^2] = 48.6 litre

Water = 60 -48.6 = 1.4 litre


बर्तन में दूध = 60 लीटर 6 लीटर दूध निकाला जाता है और 6 लीटर पानी डाला जाता है इसका मतलब है 10 प्रतिशत दूध निकाला जाता है तो मिश्रण में 54 लीटर दूध + 6 लीटर पानी होता है फिर से 6 लीटर दूध निकाला जाता है और 6 लीटर पानी डाला जाता है अतः 6 लीटर दूध में 5.4 लीटर दूध + 0.6 लीटर पानी होता है क्योंकि यह एक मिश्रण है इसलिए कुल 11.4 लीटर(6 + 5.4 )दूध निकाला जाता है तो परिणाम स्वरूप मिश्रण में 48.6 लीटर दूध 11.4 लीटर पानी होता है तो दूध और पानी का अनुपात 48.6 : 11.4 मतलब 81:19



Suppose a container contains M units of Mixture of ' X ' and ' Y '  from this , R unit of  mixture is drawn off and  replaced by an equal  amount of  ingradient Y only. The  process is repeated ' n ' times , then after ' n ' repetetions.

( Amount of X left ) / (Amount of X originally present )

= ( 1 - R / M )^n

According to the problem given,   M = 60 liters, R = 6 liters,  n = 2 times

( Amount of milk left )/60 = ( 1 - 6/60)²

Amount of milk left = 60×(1 - 1/10)²

= 60× ( 9/10)²   = 60 × 9/10 × 9/10  = 48.6 liters

Amount of water = 60 - 48.6  = 11.4 liters

Ratio = 48.6 : 11.4,   =   486 : 114  Divide it with 6,    = ( 486 / 6 ) : ( 114 / 6)= 81 : 19


After 1st replacement, in 60 L mixture, milk = 54 L, water = 6 L.

So, 6 L of 1st mixture contains 5.4 L of milk and 0.5 L of water.

So after 2nd replacement, milk = (54 - 5.4) L = 48.6 L , water = (6 - 0.6 + 6) L = 11.4 L .

Hence, the final ratio of milk and water in the resulting mixture = 48.6:11.4 = 81:19   .    (Ans)


When milk is taken out and added for the first time:

Amount of milk = 54 l 

Amount of water = 6l

Now it is a mixture of milk and water .in the ratio of 9:1

So Six litres of mixture will contain 6*0.9 = 5.4 l of milk and 6*0.1=0.6 litres of water .

So total milk taken out = 6+5.4 = 11.4 

Amount of water = 6+6-0.6 = 11.4

Ratio of mixxture = 48.6 : 11.4 = 81:19


Milk in the vessel =60 litre

6 litre of milk Is taken out and 6 litre of water is added 

I. E.  10% of milk is taken out .

So the mixture contains 54 litre of milk +6 litre of water. 

Then, 6 litre of milk is taken out and 6 litre of water is added.

Actually  6 litre of milk contains 5.4 litre milk +0.6 litre of water as it is a mixture. 

Total 11.4 litre (6+5.4) of milk is taken out .

The resulting mixture contains 48.6 litre milk +11.4 Litre of water 

So the ratio of milk and water is 48.6:11.4

In this problem replacement of water is twice. Initial ratio is 0.9 Hence final ratio is 0.9*0.9=0.81 Available milk 60*0.81=48.4 Available water. 60-48.6=11.4

Vessel contain 60 ltr

Case 1  : After taking out 6 ltr milk and adding 6 ltr water 

                     Milk 54 Ltr    water 6 ltr

Case 2 : after taking out 6 ltr milk and adding 6 ltr water

                  Mixer after first case contain 60 ltr milk and when you take out 6 ltr that contain

                 54/(54+6)*6  = 5.4 ltr milk   and

                 6/(54+6)*6   =  0.6 ltr water

Case 3:    After taking 6 ltr milk and adding 6 ltr water

           Milk  54-5.4  =48.4

     Water  6-0.6+6  =  11.4

So the ratio of milk to water is 


48.6 : 11.4


Initial quantity of milk-60l Milk taken out first time=6l Water added=6l Now milk taken second time=6l Water added second time=6l Total milk taken out =6+6=12l Total pure milk left=48l Total water added=12l Ratio of milk is water = 48:12 = 4:1

Milk in the vessel  = 60 litre .

6 litre of milk is taken out and 6 litre of water is added. 

This means, 10% of milk is taken out. 

So,  the mixture contains 54 litre of milk + 6 litre of  water. 

Again,  6 litre of milk is taken out and  6 litre of water is added. 

Actually,  6 litre of milk contains 5.4 litre milk  + 0.6 litre of water  as it is a mixture. 

Therefore,  total  11.4 litre  ( 6 + 5.4 ) of milk is taken out. 

So,  the resulting mixture contains 48.6 litre milk  + 11.4 litre of water. 

So,  ratio of milk and water =    48.6  :   11.4 







Initially the quantity of pure milk  = 60 litres

Water    quantity                        =   0 litres


Total liquid                                   60 litres

Afterwards pure milk of 6 litres is removed from the vessel and 6 litres of water is added.

Now pure milk in the vessel               =   54 litres

Water in the vessel                          =      6 litres


total quantity of liquid                       =     60 litres

The ratio of pure milk to water        =   54:6=   9:1

Now again 6 litres of milk is removed.

This 6 litres of milk contains pure milk =   (9/10)*6=  5.4 Litres and 0.6 litres of water

Therfore pure milk in the vessel after the above will be 54.0 - 5.4 =           48.6 litres

Water content                                                           =  6-0.6=                5.4 litres

Now water added(after removal of milk as above = 6 litre

Total water content                                 =     5.4+6    = 11.4 litres

Therefore   final ratio of Pure milk to water=   48.6:11.4  =  81:19  

Total milk in the vessel  =  48.6+11.4      =  60 litres

Post Answer and Earn Credit Points

Get 5 credit points for each correct answer. The best one gets 25 in all.

Still looking for expert help?

Contact an expert tutor Now.

Experience: 2 Years
Education: M.Phil
City: Bangalore
Experience: 18 Years
Education: B.Tech/B.E.
City: Kolkata
Experience: 08 Years
Education: B.Tech/B.E., B.Tech/B.E.
City: Mumbai
Topic Cloud
.Net 2D Animation 3D Animation 3D Max / Maya 3D Printing Abacus Teachers Training Abacus Training ACCA ACCA Training Accent Training Accessory Making Accountancy Accounts ACET Acrobatic Acrylic Painting ACS ACT Exam Acting & Drama Actuarial Science Administrative Laws Adobe Certification Adobe Tools Advanced Excel Advanced Maths Adventure Camps Aero Modelling Aeronautical AFCAT African Painting AICEE AIEED AIEEE AIPG Exam AIPMT AJAX Training Algebra All Subjects AMAESI AMIE AMITE Android Training Angular JS Animal Yoga Animation Animation Drawing Anthropology App Store Optimization Apparel Designing Architecture Assamese Auditing AutoCAD Training B.Arch Tuition B.Com Tuition B.Ed Tuition B.Tech Tuition BA Tuition Baal Geet Bachelor of Hospital Administration (BHA) Bachelor of Tourism Administration Bag Making Ballet Ballroom Dance Bank Clerical Bank PO Banking & Finance Basic Computer Batik Art BBA BBA Entrance BBA Subjects BBA Tuition BCA Entrance BCA Subjects BCA Tuition Bead Craft Belly Bengali Bhajan Bhakti Songs Bharat Natyam Big Data & Hadoop Bio Chemistry Bio Technology Bio-informatics Bio-medical Biology BITSAT Block Painting Blog Programming Bolly Hop Bolly Jazz Bollywood Bollywood Fusion Botany Bouquet Making Break Dance Brownies Business Analytics Business English Business Etiquette Business Management Business Mathematics Business Organisation Business Studies Business System & Infrastructure Management C, C++ C# (C Sharp) CA - CPT CA - Final CA Foundation Cake Decoration Cake Making Candle Making Canvas Painting Card Making Carnatic Dance Cartooning CAT Exam CCNA Certification CEED Ceramic Painting CET CFA Cha Cha Charcoal Painting Chemical Chemistry Chhau Chinese Chocolate Making Chocolate Puddings Choreography Classes Cisco certification Civil Civil Laws Classical Vocal Classical Western Vocal CLAT Clay Craft Clay Modelling Clay Molding Clay Painting Cloud Computing CMA Intermediate CMA-CPA-ACCA-CIMA CMAT Coding & Programming Coldfusion Collage Combo Organ COMEDK Exam Commerce Subjects Communicative English Computer Computer for official job Computer Hardware Computer Science Contemporary Content Marketing Continental Cooking & Baking Corel Draw Corporate Accounting Corporate Communication Costing Crayons Painting Creative Writing Classes CSAT CSS Training CTET Cultural Music Cupcake Cutting & Pasting CWE Coaching Dandiya Data Science Data Structures DBMS & RDBMS Decoration Decoupage Defence Exams Desserts Devotional Dance Devotional Songs Dhangar Dance Digital Marketing Diya Decoration Diya Making Drawing & Painting Dreamweaver Drupal Dry Painting DTP EAMCET Economics Education Effective Communication Egyptian Painting Electrical Electronics Embedded Systems Emboss Painting English Envelope Making ERP Training Ethical Hacking Event Management EVS Fabric Craft Fabric Painting Facebook Applications Fashion Designing Fashion Study FDDI Film Making Finance Financial Management Fine Art Fitness Centre Flash Floor Exercise Flower Making Folk Art Food & Nutrition Forest Department Exam Forex Trading Frame Making French Fusion Garba GATE Exam Gaudiya Nritya General Knowledge Geography Ghazal GIC Glass Craft Glass Painting GMAT GOAT Gondhal GPAT Graphic Designing GRE GST Training Gujrati Folk Hardware Training Hariyanvi Folk Harmonium Hindi Hindustani Vocal Hip Hop HIPAA Training History Home Science Hotel Management Hotel Management Entrance HR/Personnel HTML Training Human Resource and Marketing IAS Preparation IBM Training IBPS ICWA & ICWAI IELTS IIT JAM IIT JEE Advanced IIT JEE Mains Illustrator Income Tax Indian Classical Dance Indian Contemporary Indian Folk Indian Modern Dance Indian National Mathematical Olympiad (INMO) Informatica Informix Training Instrumental Instrumentation Insurance Exams Interior Designing iOS Training IT & Computer Subjects Japanese Java and J2EE Java Script Jazz JECA Exam Joomla Training Journalism/Writing jQuery Karnataka Folk Kathakali Kids Gym Kolattam Dance Kuchipudi Law Entrance LIC Light Vocal LLB Logic M.Com Tuition M.Ed Tuition M.Sc Tuition M.Tech Tuition Magento Training Management Subjects Manipuri Marathi Folk Martial Arts Mass communication Mathematics MATLAB MBA MBA Entrance MBBS Tuition MCA MCA Entrance MCA Entrance Exam (JECA) MCA Subjects MCAT MDS Exam Mechanical Mechanics Medical Transcription Mehendi MicroBiology Microsoft Certification Mocktail Mohiniyattam MongoDB MS Office Nattuvangam NDA NEET NEST NET Networking NID NIOS NISM NMSQT No Flame Cooking NPTT NTT Olympiad Exam Preparation Oracle Certification Oracle Training Organic Chemistry Perl Programming Personality Development PG Diploma PG Medical Pharmacy Philosophy Photography Photoshop PHP and MySQL Physical Development Physics Physiology Pilates PL/SQL Play Gym Political Science Polytechnic Pop Classes Power Yoga Programming Language Project Management PSU Exam Psychology PTT Public Speaking Python Programming Railways Exams Rajasthani Folk Rangoli Reading Skills Regional Mathematical Olympiad (RMO) Retail Management RHCE Training Robotics Rock n Roll RRB Sales Training Salesforce CRM Santoor SAP Training SAS Certifications SAT Sattriya SBI Exam School level computer Science Selenium Training Semi Classical Dance Semi Classical Vocal Shell Scripting Shetkari Shlokas Singing Six Sigma Certification Training Social Studies Sociology Soft Skills Software Engineering Software Testing Special Effects Speech & Drama Spoken English Squash SSB Exam SSC Exams Statistics Stenography and Shorthand Stock & Share Trading Story Telling Sub-Inspector Exam Sufi Sugam Sangeet Sugar CRM Sun Certification Swimming Tally ERP 9 Tango Tap Textile Designing TISS BAT Exam TOEFL TOEIC Traditional UGC Exams UGC Net Unix/Linux UPSC Exam Urdu Vedic Maths Vegetarian Video Editing Visual Basic Vmware Waltz WBCS WBJEE Web Designing Web Development Weblogic Websphere Wordpress Training Writing Skills XAT Yoga Zend Framework Zoology Zumba

Query submitted.

Thank you!

Drop Us a Query:

Drop Us a Query