21. In a class, the ratio of number of girls to boys is 1:2. If the average weight of boys is 55 kg and the average weight of girls and boys is 50 kg then find the average weight of girls.
Solution:-
22. Ankit buy a book at 4% discount and a pen at 12% discount. He overall gets a discount of 10%. If the marked price of both are 200 Rs. then find the price of the pen.
Solution:-
23. How many kg of sugar at 47 paise per kg must a man mix with 25 kg of sugar at 20 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay ?
Solution:-
SP of the mixture = 40
∴ CP of the mixture = 40×\(\frac{100}{125}\) = 32
24. The ratio of the number of boys and girls in a school was 5:3. Some new boys and girls were admitted to the school, in the ratio 5:7. At this the total number of students in the school become 1500 and the ratio of boys to girls changed to 7:5. Find the number of students in the school before new admission ?
Solution:-
25. A and B are two alloy of copper and Tin prepared by mixing metals in proportion 7:2 and 7:11 respectively. If equal quantities of alloy are melted to form a third alloy C then find the proportion of copper and tin in alloy C.
Solution:-
∴ Proportion of copper and tin in alloy C = \(\frac{14 + 7}{4 + 11} = \frac{21}{15}\) = 7 : 5 Ans
26. Find the ratio of quantities of sugar, in which sugar costing 25 per kg and 20 per kg should be mixed so that there will be neither loss nor gain on selling the mixed sugar at the rate of 22 per kg.
Solution:-
S.P. of mixed sugar = 22 per kg
Since there is neither loss nor gain
Hence C.P. of mixed sugar = 22 per kg
Now using alligation method
27. A merchant borrowed Rs. 2500 from two money lenders. For one loan he paid 12% p.a. and for the other 14% p.a. The total interest paid for one year was Rs. 326. How much did he borrowed at each rate?
Solution:-
overall interest rate = \(\frac{326}{2500} \times 100\% = \frac{326}{25}\% \)
∴ amount given on 12% rate = \(\frac{25}{12 + 13} \times 12\) = 1200 Ans
& amount given at 14% rate = 2500-1200 = 1300 Ans
28. A vessel contains 96 litres of milk. 12 litres of milk is taken out from it and replaced by water then again from the mixture, 12 litre is taken out and replaced by water. Then find the ratio of milk and water in the resultant mixture ?
Sol:
Remaining amount of milk = initial quantity\({\left( {1 – \frac{{quantity\;taken\;out}}{{initial\;quantiy}}} \right)^n}\)
= 96\({\left( {1 – \frac{{12}}{{96}}} \right)^2}\)
= 96\({\left( {1 – \frac{{1}}{{8}}} \right)^2}\)
= 96×\(\frac{7}{8}\)×\(\frac{7}{8}\) = 73.5
quantity of water = 96 – 73.5
= 22.5
∴ required ratio ⟹ 96 : 73.5
= 49 : 15 Answer
29. 112 litres of a mixture contains milk and water in the ratio of 27:5. How much more water is to be added to get a mixture containing milk and water in the ratio of 3:1 ?
Sol:
30. A and B are two alloy of Gold and Copper prepared by mixing metals in the ratio 5:3 and 5:11 respectively. Equal quantities of these alloys are melted to form a third alloy C then find the ratio of Gold & Copper in the alloy C ?
Sol: