Uses of Ratios and Proportions

Q.

$\mathrm{A}$ and $\mathrm{B}$ are partners sharing profits and losses in the ratio of $3:2$. They admit $\mathrm{C}$ into the partnership for one-fourth share of the profits while $\mathrm{A}$ and $\mathrm{B}$ as between themselves are sharing profits & losses equally. Find the new profit sharing ratio and sacrificing ratio.

Q. The salaries of A, B and C are in the ratio $1:3:4$. If the salaries are increased by $5$%, $10$% and $15$% respectively, then the increased salaries will be in the ratio:

1. $20:66:95$
2. $21:66:95$
3. $21:66:92$
4. $19:66:92$

Q. 20 pens are divided between A and B in the ratio 3:2. Find their respective shares.

1. 10, 10
2. 8, 12
3. 12, 8
4. 6, 14

Q.

Out of $1800$ students in a school, $750$ opted basketball, $800$ opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of

(a) Number of students who opted basketball to the number of students who opted table tennis.

(b) Number of students who opted cricket to the number of students opting basketball.

(c) Number of students who opted basketball to the total number of students.

Q. The ratio of income to the expenditure of a family is $7:6$. Find the savings if the income is Rs. $14000.$

Q.

The angles of a triangle are in the ratio 1 : 2 : 3, find the measure of each angle of the triangle.​

Q. The incomes of $A$ and $B$ are in the ratio $5:3.$ The expenses of $A,B$ and $C$ are in the ratio $8:5:2.$ If C spends $Rs.2000$ and $B$ saves $Rs.700,$ then $A$ saves

1. $Rs.1000$
2. $Rs.250$
3. $Rs.500$
4. $Rs.1500$

Q. The ratio of the prices of two houses $A$ and $B$ was $4:5$ last year. This year the price of $A$ increased by $25\%$ and that of $B$ by Rs $50,000$. If their prices are now in the ratio $9:10$, then the price of $A$ last year was

1. Rs $3,60,000$
2. Rs $4,50,000$
3. Rs $4,80,000$
4. Rs $5,00,000$

Q. Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.