Equal Ratio

Q.

A photographer is taking a picture of a bride and groom together with $6$ attendants. How many ways can he arrange the $8$ people in a row if the bride and groom stand in the middle?

Q.

Two equivalent ratios for $3:7$.

Q. The ages of A and B are in the ratio 3: 1. After fifteen years, the ratio will be 2: 1. Their present ages are respectively.

1. 45 years, 90 years
2. 45years, 15 years
3. 36 years, 12 years
4. 33 years, 11 years

Q.

If

$$\begin{gathered} 3+3\alpha +3{\alpha }^2+\dots .\infty =45/8, \\ \alpha >0 \end{gathered}$$

then the value of α will be

1. $15/23$

2. $7/15$

3. $7/8$

4. $15/7$

Q.

Find two equivalent ratios of $5:3$

Q. If x is the mean proportion of 25 and 4, then find the value of x.

1. 100
2. 25
3. 10
4. 50

Q.

In which of the following case, do the quantities vary directly with each other?

1. $x$	$0.5$	$2$	$8$	$32$
   $y$	$2$	$8$	$32$	$128$

2. $p$	$1^2$	$2^2$	$3^2$	$4^2$
   $q$	$1^3$	$2^3$	$3^3$	$4^3$

3. $r$	$2$	$5$	$10$	$25$	$50$
   $s$	$25$	$10$	$5$	$2$	$0.5$

4. $u$	$2$	$4$	$6$	$9$	$12$
   $v$	$18$	$9$	$6$	$4$	$3$

Q.

Joseph bought two varieties of rice, costing 6 cents per ounce and 8 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 10 cents per ounce, making a profit of 50 percent. What was the ratio of the mixture?

1. 1: 5

2. 1: 4

3. 2: 5

4. 2:1

Q. The mean proportion between 5:45 is _____.

1. 25
2. 15
3. 5
4. 115

Q.

Both $xandy$ vary directly with each other and when $xis10,yis14$, which of the following is not a possible pair of corresponding values of $xandy$?

1. $25and35$

2. $35and25$

3. $35and49$

4. $15and21$

Q.

Fill in the blanks

$2:3=8:\_$

Q. Factorise : $x^4-625$

Q. If $\frac{2x^2-6x+4}{4x^2-10x+3}$ = $\frac{x^2-3x}{2x^2-5x}$ , value of x is for $x\ne$0.

1. $\frac{11}{5}$
2. $\frac{5}{11}$
3. 11
4. 5

Q. Equivalent ratio of $\frac{3}{7}$ is .

1. $\frac{12}{27}$
2. $\frac{9}{22}$
3. $\frac{15}{35}$
4. $\frac{18}{49}$

Q. It takes 6 men 5 hours to build a car. How long does it take for 3 men?

1. 5 Hours
2. 20 Hours
3. 1 Hour
4. 4 Hours

Q.

If a : b = 5 : 3, find (2a + 7b) : (6a - 7b).

1. 12:9

2. 31:9

3. 25:9

4. 22:7

Q.

We measured the thickness of a sheet by the Venire Calipers in successive measurement. The readings turned out to be 1.2 mm, 1.4 mm, 1.5 mm, 1.8 mm and 1.6mm. Calculate the absolute error, relative error and percentage error

Q.

Neha's toy car can travel 288 meters in a minute while Vendetta's toy car can travel 24.48 kilometres in an hour. The ratio of the speed of the cars belonging to Neha and Vendetta is:

1. 12:17

2. 17:12

3. 13:19

4. 4:7

Q. If 25 is the mean proportion between 5 and X, then X is equal to____.

1. 125
2. 45
3. 12.5
4. 15

Q.

If $\frac{3x-4y}{2x-3y}=\frac{5x-6y}{4x-5y}$, find x : y.

1. 1:1

2. 3:3

3. 4:4

4. 2:2

Q.

If the cost of 48 bags of paddy is Rs 16, 800, then cost of 36 bags of paddy is Rs__________

1. 12, 800

2. 14, 800

3. 14, 600

4. 12, 600

Q.

Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

1. 4 cm

2. 6 cm

3. 9 cm

4. 8.2 cm

Q. Solve by factorization
$a^2{x}^2+(a^2+b^2)x+b^2=0,a\ne 0$

Q. Factorise : $x^3-512$

Q.

The ratio of areas of a circular and rectangular field is $1:2$. Find the area of the rectangular field if the area of a circular field is $50$ m².

1. $25$ m²

2. $50$ m²

3. $100$ m²

4. $75$ m²

Q. Factorise : $x^2-2+\frac{1}{x^2}-y^2$

Q.

A father wants to divide ₹ 1800 among his sons in the ratio of their ages. If one son is 12 years old and the other is 15 years old, then their respective shares would be

1. ₹ 500, ₹ 700

2. ₹ 300, ₹ 600

3. ₹ 1200, ₹ 1500

4. ₹ 800, ₹ 1000

Q.

If an SUV can transport 7 people, car can transport 5, jeep can transport 8 and auto can transport 2 people, which of the following combination can be used to exactly transport 25 people?

1. Two rounds of jeep, one round of SUV and one round of auto.

2. 2 rounds of SUV, 2 rounds of car

3. One round of SUV and jeep each, two rounds of car

4. Three rounds of car, two rounds of SUV and on round of jeep

Q. Factorise : $\frac{64}{12}{a}^3-\frac{96}{25}{a}^2+\frac{48}{5}a-8$

Q. Factorise : $216x^3+\frac{1}{125}$