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. Ans