Ratio

Q.

A total of Rs. 10, 000 is distributed among 150 persons as gift. A gift is either of Rs. 50 or Rs. 100. The total number of Rs. 50 gifts is _________.

___

Q. Fill in the blanks of the following

(i) $\frac{x}{7}=\frac{y}{3}=\frac{3x+5y}{..........}=\frac{7x-9y}{.........}$

(ii) $\frac{a}{3}=\frac{b}{4}=\frac{c}{7}=\frac{a-2b+3c}{.......}=\frac{..........}{6-8+14}$

Q. 5. If 45% of a number is added to another number, the first number becomes 135 times of the another number. What is the ratio of these two numbers?

Q. a dealer sells a toy for rs.24 and gains as much as percent as the cost price of the toy . find the cost price of the toy

Q. If $a+b+c=0$, then $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=$ ____.

1. 3

Q. If $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ where $(a+b+c)\ne 0$ and $abc\ne 0$. What is the value of $(a+b)(b+c)(c+a)?$

1. $0$
2. $1$
3. $-1$
4. $2$

Q. What number must be added to each term of the ratio 2 : 5, so that it may become equal to 5 : 6.

Q. If $\frac{15a^2+4b^2}{15a^2-4b^2}=\frac{47}{7}$ then find the values of following ratios.

(i) $\frac{a}{b}$ (ii) $\frac{7a-3b}{7a+3b}$ (iii) $\frac{b^2-2a^2}{b^2+2a^2}$ (iv) $\frac{b^3-2a^3}{b^3+2a^3}$

Q. The sum of three numbers is $98$. If the ratio of the first to second is $2:3$ and that of the second to the third is $5:8$, then the second number is:

Q.

The digits of a positive number have 3digits which are in A.P. and their sum is 18.

The number obtained by reversing digits is 594 less than the original number.

Find the number.

Q.

If a and b are in a ratio, then how they are represented symbolically?

1. %

2. :

3. #

4. *

Q. 27a² $-$ 75b²

Q. If Mitu is dropped out of the market, what will be new market demand schedule?

Price (Rs.)	Demand schedule of mohan (Units)	Demand schedule of Rohan (Units)	Demand Schedule of Mitu (Units)
1 2 3 4 5	60 50 40 30 20	55 40 25 10 0	24 13 5 0 0

Q. Give the correct percentage
(a) $\frac{80}{100}=$ %
(b) $\frac{42}{100}=$ %
(c) $\frac{8}{100}=$ %

Q. Two numbers are in ratio of $1:5$. Sum of the numbers is $36$. Find the larger number.

1. $3$
2. $9$
3. $30$
4. $18$

Q.

A's weight is 50 kg more than that of B. What is the ratio of A's weight to B's weight? (Take B's weight as x)

1. $(x+50):x$

2. $x:(x+50)$

3. $x:50x$

4. $50x:x$

Q.

A piece of string $175cm$ in length was cut into two pieces, the ratio of whose length was $5:2.$ Find the length of each piece.

Q. The adjacent sides of a rectangle are in the ratio 5 : 3 and the area of the rectangle is 29.4 sq.cm. Find the length and breadth of the rectangle.

Q. $ABCDE$ is a pentagon in which $AE$ is parallel to $BC,\angle C={153}^{\circ },\angle D=x^{\circ }$ and $\angle E={\left(2x\right)}^{\circ }$. Find the value of $x$.

1. $x=88$
2. $x=69$
3. $x=61$
4. $x=55$

Q. Inscribe a regular pentagon in a circle of radius $3cm$. The interior angles of the pentagon are:

1. ${54}^{\circ }$
2. ${60}^{\circ }$
3. ${162}^{\circ }$
4. ${108}^{\circ }$

Q. If $(x^2-y^2)=18$ and $(x-y)=3$, find the value of $16x^2{y}^2$.

1. 27
2. 81
3. 243
4. 729

Q. A badminton player won 6 games and lost 4.The fraction of the games he won is

1. $\frac{6}{4}$
2. $\frac{4}{6}$
3. $\frac{5}{10}$
4. $\frac{6}{10}$

Q. How much water must be added to $300$ litre of a solution so that its concentration may change from $25\%$ to $20\%$?

1. $70$ litre.
2. $75$ litre.
3. $67$ litre.
4. $98$ litre.

Q. (a $-$ b)² + 8(a $-$ b) + 15

Q. a fruit seller brought some watermelons at rupees 8 each . out of these , five were broken .he sold the remaining at rupees 15 each and made a gain of rupees 275. how many watermelons did he buy?

Q. Rohit, Lohit and Mohit started a business by investing in the ratio 1/3 : 2/4 : 2/5. After 8 months Mohit withdrew 1/2 of his investment. If after 12 months from start of business Rohit and Lohit got a share of Rs 16, 000 out of the total profit, then find the share of Mohit?