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
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:-