This set contains Mixture and Alligation Questions with Solutions — Set 2 (Q11 to Q20) covering a mix of question types and difficulty levels — from basic to advanced — exactly as asked in real competitive exams.
Solutions are written in a simple, step-by-step notebook style for easy self-study and quick understanding. Each solution is broken down step by step so even the toughest question feels easy. These questions are hand-picked for students preparing for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and all campus placement aptitude tests. International students preparing for GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests will find these equally useful.
✏️ Attempt each question on your own first — then check the solution below.
Mixture and Alligation Questions 11 to 20 with Solutions
11. In two alloys A and B the ratio of zic to tin is 5:2 and 3:4 respectively. 7kg of alloy A and 21kg of the alloy B are mixed together to form a new alloy. What will be the ratio of zinc and tin in the new alloy ?
12. Three vessels whose capacities are in the ratio 3:2:1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5:2, 4:1 and 4:1 respectively. Taking \(\frac{1}{3}\) of first, \(\frac{1}{2}\) of second and \(\frac{1}{7}\) of the third mixtures, a new mixture kept in a new vessel is prepared. Find the % of water in the new mixture ?
13. 60 kg of alloy A is mixed with 100 kg of alloy B. If alloy A has lead and copper in the ratio 3:2 and alloy B has copper and tin in the ratio 1:4, then find the amount of copper in the new alloy.
14. Two variety of tea costs Rs. 35 per kg and Rs. 40 per kg respectively are mixed in the ratio 2:3 by weight. If one-fifth of the mixture is sold at Rs. 46 per kg and remaining at the rate of Rs. 55 per kg, then find the profit percent.
15. 30 litres of a mixture contains milk & water in the ratio 4:1. Then find the amount of milk to be added to the mixture so as to have milk and water in the ratio 6:1.
16. A man purchased two books in Rs. 1000. He sells the first book at \(\frac{4}{5}\) of its cost price and the second book at \(\frac{5}{4}\) of its cost price. If during the whole transaction he earns a profit of Rs. 100 then find the cost price of cheaper book.
17. Silver is 19 times as heavy as water and copper is 10 times as heavy as water. In what ratio these be mixed to get an alloy 13 times as heavy as water ?
18. Ankit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20% and pen at a loss of 10%. If his overall profit is 240 then find the cost price of each pencil and each pen.
19. Ratio of land and water on earth is 1:2 and ratio of land and water in northern hemisphere is 2:3 then find the ratio of land and water in southern hemisphere.
20. In what proportion must water be mixed with spirit to gain 40% by selling it at cost price.
Solutions — Mixture and Alligation Questions 11 to 20
11. In two alloys A and B the ratio of zic to tin is 5:2 and 3:4 respectively. 7kg of alloy A and 21kg of the alloy B are mixed together to form a new alloy. What will be the ratio of zinc and tin in the new alloy ?
Solution:-
method (2):
∴ in new alloy tin : alloy = 1 : 2
∴ zinc : tin = 1 : 1 Ans
12. Three vessels whose capacities are in the ratio 3:2:1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5:2, 4:1 and 4:1 respectively. Taking \(\frac{1}{3}\) of first, \(\frac{1}{2}\) of second and \(\frac{1}{7}\) of the third mixtures, a new mixture kept in a new vessel is prepared. Find the % of water in the new mixture ?
Solution:-
method (1): Let the capacity of vessels be 3 litres, 2litres and 1 litre respectivelty.
when we mix these three vessels then in new vessel
milk = \(\frac{5}{7} + \frac{4}{5} + \frac{4}{35} = \frac{57}{35}\)
water = \(\frac{2}{7} + \frac{1}{5} + \frac{1}{35} = \frac{18}{35}\)
total new mixture = \(\frac{57}{35} + \frac{18}{35} = \frac{75}{35} = \frac{15}{7}\)
∴ % of water = \(\frac{\frac{18}{35}}{\frac{15}{7}} \times 100 = 24\% \) Ans
13. 60 kg of alloy A is mixed with 100 kg of alloy B. If alloy A has lead and copper in the ratio 3:2 and alloy B has copper and tin in the ratio 1:4, then find the amount of copper in the new alloy.
14. Two variety of tea costs Rs. 35 per kg and Rs. 40 per kg respectively are mixed in the ratio 2:3 by weight. If one-fifth of the mixture is sold at Rs. 46 per kg and remaining at the rate of Rs. 55 per kg, then find the profit percent.
Solution:
method(1):
Let 5 kg of mixture be prepared.
∴ CP of 5 kg of mixture = 2×35 + 3×40 = 190
total SP of 5 kg of mixture = 46 + 4×55 = 266
∴ profit % = \(\frac{266 – 190}{190} \times 100\) = 40% Ans
∴ profit % = \(\frac{53.2 – 38}{38} \times 100\) = 40% Ans
15. 30 litres of a mixture contains milk & water in the ratio 4:1. Then find the amount of milk to be added to the mixture so as to have milk and water in the ratio 6:1.
Solution:
16. A man purchased two books in Rs. 1000. He sells the first book at \(\frac{4}{5}\) of its cost price and the second book at \(\frac{5}{4}\) of its cost price. If during the whole transaction he earns a profit of Rs. 100 then find the cost price of cheaper book.
Solution:-
17. Silver is 19 times as heavy as water and copper is 10 times as heavy as water. In what ratio these be mixed to get an alloy 13 times as heavy as water ?
Solution:-
18. Ankit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20% and pen at a loss of 10%. If his overall profit is 240 then find the cost price of each pencil and each pen.
Solution:-
overall profit % = \(\frac{240}{2400} \times 100\) = 10%
19. Ratio of land and water on earth is 1:2 and ratio of land and water in northern hemisphere is 2:3 then find the ratio of land and water in southern hemisphere.
Solution:-
on earth \(\frac{water}{water + land} = \frac{2}{3}\)
on N.H. \(\frac{water}{water + land} = \frac{3}{5}\)
Let on S.H. \(\frac{water}{water + land} = x\)
⟹ \(x – \frac{2}{3} = \frac{1}{15}\) ⟹ \(x = \frac{11}{15}\)
∴ on S.H. \(\frac{water}{water + land} = \frac{11}{15}\implies \frac{water}{land} = \frac{11}{4}\)
∴ required ratio = 11:4 Ans
20. In what proportion must water be mixed with spirit to gain 40% by selling it at cost price.
Solution:-
Let C.P. of spirit = x
∴ S.P. of mixture = y
Let C.P. of mixture = y
∴ \(\frac{x – y}{y} = \frac{40}{100} = \frac{2}{5}\)
5x – 5y = 2y ⟹ y = \(\frac{5}{7}x\)
required ratio of water and spirit = 2:5 Ans
⬤ In these type of questions covert % into ratio, that will be the answer. Answer
✅ Well done on completing Set 2!
Continue practising with Mixture and Alligation Questions 21 to 30 → Set 3 or revisit the Mixture and Alligation Concept Page to strengthen your formulas and tricks before moving ahead.
Consistent practice is the key to mastering mixture and alligation for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and international exams including GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests. Want to understand the concept better? Read about Mixture on Wikipedia before attempting the next set.
This page is part of our complete series of mixture and alligation questions with solutions for competitive exams — covering every question type from basic to advanced so you can build speed, accuracy and confidence. Practising these questions regularly will also strengthen your core mixture and alligation concept before your exam day.