   Question Answers

# Three containers have their volumes in the ratio 3:4:5. They are full of milk and water. The mixtures contain milk and water in the ratios of 4:1, 3:1 and 5:2, respectively. The ratio of milk and water in the fourth container which contains all these mixtures is [a] 4:1[b] 151:48[c] 157:53[d] 5:2  Hint: Assume that the volumes of the containers are 3x,4x and 5x. Find the content of milk and water in each of these solutions. Hence find the content of milk and water in the final solution. Hence find the ratio of the content of milk to the content of water.

Complete step-by-step solution -

Let the volume of the first container be 3x, the volume of the second container be 4x, and that of the third container be 5x.
Amount of milk in the first container $=\dfrac{4}{1+4}3x=\dfrac{12x}{5}$
Amount of milk in the second container $=\dfrac{3}{3+1}4x=\dfrac{12x}{4}=3x$
Amount of milk in the third container $=\dfrac{5}{5+2}5x=\dfrac{25x}{7}$
Amount of water in the first container $=\dfrac{1}{4+1}3x=\dfrac{3x}{5}$
Amount of water in the second container $=\dfrac{1}{3+1}4x=x$
Amount of water in the third container $=\dfrac{2}{2+5}5x=\dfrac{10x}{7}$
Hence the total amount of milk in the final container $=\dfrac{12x}{5}+3x+\dfrac{25x}{7}=\dfrac{84x+105x+125x}{35}=\dfrac{314x}{35}$
The total amount of water in the final container $=\dfrac{3x}{5}+x+\dfrac{10x}{7}=\dfrac{21x+35x+50x}{35}=\dfrac{106x}{35}$
Hence the ratio of the amount of milk to the amount of water in the fourth container $=\dfrac{314x}{35}:\dfrac{106x}{35}=314:106=157:53$
Hence option [c] is correct.

Note: Alternatively, you can find the ratio of milk to the total volume and hence find the ratio of milk to water.
Let the total volume of the final solution be (3+4+5)=12.
So we have the amount from the first solution = 3
Hence milk from the first solution $=\dfrac{12}{5}$
Similarly milk from the second solution $=3$ and the milk from the third solution $=\dfrac{25}{7}$
Hence total milk $=\dfrac{12}{5}+3+\dfrac{25}{7}=\dfrac{314}{35}$
Hence the ratio of milk to the total volume $=\dfrac{314}{35}:12=\dfrac{157}{35}:6=157:210$
Hence the ratio of milk to water $=157:\left( 210-157 \right)=157:53$

CBSE Class 10 Maths Chapter 13 - Surface Areas and Volumes Formula  Respiratory and Lung Volumes  CBSE Class 9 Maths Chapter 13 - Surface Areas and Volumes Formulas  CBSE Class 6 Maths Chapter 12 - Ratio and Proportion Formulas  Ratio and Proportion Formula  Poisson's Ratio  Sacrificing Ratio  Ratio Analysis Formulas  Excretory Products and Their Elimination  Physical Properties of Alkanes and Their Variations  Important Questions for CBSE Class 6 Maths Chapter 12 - Ratio and Proportion  CBSE Class 6 Science The Living Organisms and Their Surroundings Worksheets  Important Questions for CBSE Class 10 Maths Chapter 13 - Surface Areas and Volumes  Important Questions for CBSE Class 6 Science Chapter 9 - The Living Organisms and Their Surroundings  Important Questions for CBSE Class 9 Maths Chapter 13 - Surface Areas and Volumes  Important Questions for CBSE Class 12 Maths Chapter 11 - Three Dimensional Geometry  Important Questions for CBSE Class 10 Maths Chapter 10 - Circles  Important Questions for CBSE Class 11 Maths Chapter 12 - Introduction to Three Dimensional Geometry  Important Questions for CBSE Class 11 Chemistry Chapter 10 - The s-Block Elements  Important Questions for CBSE Class 8 Maths Chapter 13 - Direct and Inverse Proportions  CBSE Class 10 Maths Question Paper 2017  CBSE Class 10 Maths Question Paper 2020  Maths Question Paper for CBSE Class 10 - 2011  Maths Question Paper for CBSE Class 10 - 2008  Maths Question Paper for CBSE Class 10 - 2012  Maths Question Paper for CBSE Class 10 (2016)  Maths Question Paper for CBSE Class 10 - 2009  Maths Question Paper for CBSE Class 10 - 2010  Maths Question Paper for CBSE Class 10 - 2007  CBSE Class 10 Maths Question Paper 2018 - Free PDF  RD Sharma Solutions for Class 10 Maths Chapter 16 - Surface Areas and Volumes  NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes  NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes  NCERT Solutions for Class 6 Maths Chapter 12  NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes in Hindi  NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion in Hindi  RS Aggarwal Class 6 Solutions Chapter-10 Ratio, Proportion and Unitary Method  NCERT Exemplar for Class 6 Maths Solutions Chapter 8 Ratio & Proportion  RS Aggarwal Solutions Class 6 Chapter-10 Ratio, Proportion and Unitary Method (Ex 10A) Exercise 10.1  RD Sharma Class 6 Maths Solutions Chapter 9 - Ratio, Proportion and Unitary Method  