Uses of Ratios and Proportions

Q.

Simplify and solve the following linear equation: $0.25(4f-3)=0.05(10f-9)$

Q.

There are $750$ students in a school. If $25$students stand in each row during morning assembly, then find the number of rows.

Q.

Question 10

Raju purchases 10 pens for Rs. 150 and Manish buys 7 pens for Rs. 84. Can you say who got the pen cheaper?

Q.

Solve the following:

$\frac{8}{x}=\frac{5}{x-1}$

Q.

The ratio of the diameter of a circle to its circumference is ____.

1. 1 : 1
2. π : 1
3. 1 : π
4. Varies with the radius of the circle

Q.

A watch gains $5$ seconds in $3$ minutes was set right at $7\mathrm{AM}$ In the afternoon of the same day, when the watch shows a quarter past $4$ oclock, the true time is ______________.

Q.

If $m\left[\begin{array}{cc}-3& 4\end{array}\right]+n\left[\begin{array}{cc}4& -3\end{array}\right]=\left[\begin{array}{cc}10& -11\end{array}\right]$ , then $3m+7n$ is equal to

1. $3$

2. $5$

3. $10$

4. $1$

Q.

Write a ratio of $2yearsto6months$

Q.

The sum of $0.2+0.22+0.222+.............$ to $n$ terms is equal to

Q.

Question 64

The students of a school belonging to different religious backgrounds. The number of Hindu students is 288, the number of Muslim students is 252, the number of Sikh students is 144 and the number of Christian students is 72. Find the ratio of

a) The number of Hindu students to the number of Christain students.

b) The number of Muslim students to the total number of students.

Q.

Solve the following equations.$3x-2(2x-5)=2(x+3)-8$. Also, verify.

Q.

When one is added to each of the two numbers their ratio becomes $1:2$ and when $5$ subtracted from each of them their ratio becomes $5:11$.Find the numbers.

Q.

An alloy contains only Zinc and Copper and they are in the ratio of 7:9.

If the weight of the alloy is 8 kg, then find the weight of Copper in the alloy

Q.

Question 62

In a school, the ratio of the number of large classrooms to small classrooms is 3:4. If the number of small rooms is 20, then find the number of large rooms.

Q.

A guy walks into a store and steals $Rs100$ from the store without the owners knowledge. He then buys $Rs60$ worth of goods using that $Rs100$ and the owner gives $Rs40$ in change. How much money did the owner lose?

Q.

In a village, males and females are in the ratio $12:11$. What part of total population are females in the village?

Q.

A rectangular sheet of paper is of length 1.2 m and width 21 cm. Find the ratio of the width of the paper to its length.

Q.

Find the values of the ratios (red to blue) of the perimeters and areas of the similar figures.

Q.

Question 7(a)

Find the ratio of the following:

30 minutes to 1 hour

Q.

Question 32

State whether the given statements are true (T) or false (F).

A ratio can be equal to 1.

Q.

Cost of a toffee is $50$ Paise and the cost of a chocolate is $₹10$, What will be the ratio of the cost of a toffee to the cost of a chocolate?

1. $1:5$

2. $5:1$

3. $1:20$

4. $20:1$

Q.

An alloy consists of zinc and iron in the ratio $3:5.$ How much iron is there in $40kg$ of the alloy $?$

Q.

Question 47

The marked price of a table is Rs. 625 and its sale price is Rs. 500. What is the ratio of the sale price to the marked price?

Q.

Solve:$4+5(p-1)=34$

Q.

Check whether the given terms $2,3,4,5$ are in proportion.

Q.

$x+3\left|x\right|=10$. Find the value of $x$.

Q.

Find the ratio of $40$ minutes to $1.5$hours.

Q.

Solve the following equation by factorisation:

$1=\frac{1}{2}{x}^2-\frac{7}{6}x$

Q.

On a peepal tree there are thirteen branches and on each branch there lived fourteen birds. If twice as many of the parrots were the crows and twice as many of the crows were the sparrows, then the number of

sparrows$=\underline{}.$

Parrots$=\underline{}.$

crows$=\underline{}.$

Q. There are 20 boys and 25 girls in a class. If 5 girls are added to the class, what is the new ratio of number of boys to the girls?

1. 4 : 5
2. 1 : 1
3. 2 : 3
4. 3 : 2