Q1:

If $(a^3+b^3):(a^2-ab+b^2)=5:2$ and$(a^2-b^2):(a+b)=7:4$.Find a:b

Q2:

Three friends Amit, Mayank and Nitesh, started a business by investing money in a ratio 5:8:16, next year they increased their investments by 25%, 37.5%and 20% respectively. In what ratio the profit earned in the second year should be distributed among Amit, Mayank, and Nitesh?

Q3:

Mr Rajveer purchased a unique diamond called "Zoinoor", which was very expensive and the cost of the diamond is proportional to square of its weight. But he accidently broke the diamond and it was split into three pieces which were in ratio of 3:2:1 by weight. If he incurred a total loss of Rs 46200 due to the accident, find the initial cost of diamond.

Q4:

Arun and Varun participated in a race. For every ten steps of Varun, Arun takes eight steps, and five steps of Arun is equal to seven steps of Varun. Find the ratio of the speed of Arun and Varun.

Q5:

The perimeter of a quadrilateral is 243 cm. If the sides of the quadrilateral are in ratio $\frac{2}{3}:\frac{5}{6}:\frac{7}{10}:\frac{1}{2}$.Find the difference of the sum of two smaller sides to that of the two larger sides.

Q6:

Some chocolates were distributed among three friends in such a manner that Rajesh received $\frac{2}{3}r\mathrm{d }$of chocolates as Rakesh received and Rakesh received $\frac{1}{2}$as much as Roshan received. What fraction of the total chocolates was received by Rakesh?

Q7:

The monthly income of A and B are in ratio 5:8. The ratio of their expenditure is 2:3 and their combined saving is Rs 5000 per month. If the income of A and B is increased by 20% and 25% respectively and their spending remains unchanged, then their combined saving increased by 60%. Find the ratio of their new income to that of their new saving. 

Q8:

A paint bucket is filled with 3 parts of paint and one part of solvent. What percentage of the mixture must be drawn off and replaced by the solvent to make the mixture 50% paint and 50% solvent?

Q9:

A bag has Rs 105 in the denomination of Rs 2 and Re 1 such that the ratio of money from Rs 2 and Re 1 is in the ratio 8:7. A man withdrew Rs 28 of the bag such that equal amount of money from each denomination was taken out and replaced with 5 one rupee coin. Find the ratio of Rs 2 and Re 1 coin finally in the bag.

Q10:

If $\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=\frac{2a-3b+5c}{K}$ .Find the value of K.

Q11:

Find the ratio in which glucose and lactose be mixed to get the concentration of sugar as that of maltose?

Q12:

‘A’ invests 25% of his money in four companies L, I, J and K in the ratio$\frac{1}{7}:\frac{5}{14}:\frac{3}{8}:\frac{1}{8}$. If after a year, the profit percent earned by four companies are 10%, 20%, 30% and 40%. Find the minimum amount A will have after a year, if the amount he invested was a three-digit whole number.

Q13:

In a country named "Wakanda", only 60% of the people are literates. Due to migration, it is expected that the number of illiterates will increase by 25% and the total population will increase by 20%. Find the new ratio of illiterates to literates.

Q14:

A, B, C and D invested Rs.5000, Rs.4500, Rs.4000 and 8000 in a business. After one year, A withdraws his entire amount, B withdraws his entire amount after 2 years, C withdraws his money after 3 years and in the end of 4^th year D also withdraws his sum of money from the business. If they earned Rs.21500 in the end of 4^th year, find A's share in the profit?

Q15:

Ankit and Aniket started a business with Ankit’s initial investment of Rs.7,000 in the business. Ankit withdraws Rs 2000 after two months and Rs 1500 after eight months. If Aniket invests a certain sum in the business at the beginning of the year, leaves it intact and receives Rs.5450 as his share of the total profit of Rs.11970 for the year, find the monthly investment of Aniket in the company.