Mix Test - 8

Let the numerator be x and the denominator be x + 3 

∴ Fraction = $\frac{x}{(x + 3)}$

According to the question, 

$\frac{(x+7)}{(x+3-2)}=2$

⇒ x + 7 = 2x + 2 

⇒ x = 7 – 2 = 5 

∴ Numerator = 5 

And denominator = 5 + 3 = 8 

∴ Sum of numerator and denominator = 8 + 5 = 13

Hence, the correct option is (B).

Given:

Cost Price = 928

Profit % = 15%

Formula:

Profit % = $\left(\frac{\mathrm{Profit}}{\mathrm{Cost} \mathrm{Price}}\right)\times 100$

Calculation:

P % = $\left(\frac{\mathrm{P}}{\mathrm{C}.\mathrm{P}}\right)$ × 100

⇒ 15 = $\left(\frac{\mathrm{P}}{928}\right)$ × 100

⇒ P = $\left(\frac{15\times 928}{100}\right)$ = 139.20

∴ The net profit = Rs. 139.20

Hence, the correct option is (B).

\(3075\) is divided by \(25\).

\(\Rightarrow \frac{3075}{25}=123\)

\(\therefore\) The quotient \(=123\)

Hence, the correct option is (B).

Given:

S.I. = Rs. 720, Rate  = 8% and Time = 9 months

Formula:

S.I. = $\frac{\mathrm{Principal}\times \mathrm{Rate}\times \mathrm{Time}}{100}$

Let the principal be P.

Here, Time = 9 months = $\left(\frac{9}{12}\right)$ years = $\left(\frac{3}{4}\right)$ years

According to the question, we have

$\frac{\left(\mathrm{P}\times 8\times {\displaystyle \frac{3}{4}}\right)}{100}=720$

⇒ 6P = 72000

⇒ P = 12000

∴ The required principal is Rs. 12000.

Hence, the correct option is (A).

Given:

Actual weight of article \(=1000 \mathrm{gm}\)

Faulty weight of article \(=800 \mathrm{gm}\)

As we know,

Profit percent due to wrong weight \(=\left[\frac{\text{ Error}}{\text{(True weight - Error)}}\right] \times 100\)

Now

Actual weight of article \(=1000 \mathrm{gm}\)

Faulty weight of article \(=800 \mathrm{gm}\)

Error \(=1000-800=200 \mathrm{gm}\)

Profit percent due to wrong weight \(=\left[\frac{\text{ Error}}{\text{(True weight - Error)}}\right] \times 100\)

\(\Rightarrow \left(\frac{200}{800}\right) \times 100=25 \%\)

\(\therefore\) The actual profit percentage is \(25 \%\).

Hence, the correct option is (B).

Given:

(3⁶¹ + 3⁶² + 3⁶³ + 3⁶⁴)

= 3⁶¹(1 + 3 + 32 + 33)

= 3⁶¹ × (1 + 3 + 9 + 27)

= 3⁶¹ × 40

= 3⁶⁰ × 3 × 4 × 10

= 3⁶⁰ × 4 × 30

∵ The above expression has 30 in it. In other words 30 is one of the factors of the given expression.

∴ 30 will divide (3⁶¹ + 3⁶² + 3⁶³ + 3⁶⁴) completely.

Hence, the correct option is (A).

Given:

The ratio of sides of two cube is 2 : 3.

Concept:

If ‘a’ be the side of a cube then total surface area of the cube is 6a².

Calculation:

The ratio of sides of two cube is 2 : 3.

Let, sides of the cube are 2a and 3a.

Total surface area of the first cube = 6 × (2a)² = 24a²

Total surface area of the second cube = 6 × (3a)² = 54a²

The ratio of the total surface area is 24a² : 54a²

= 4 : 9

∴ The ratio of the total surface area is 4 : 9.

Hence, the correct option is (B).

\(530 \times 26\)

\(\Rightarrow 530 \times 26\)

\(\Rightarrow 13780\)

\(\therefore\) The required product is \(13780\).

Hence, the correct option is (A).

The total number of girls is x

The total number of boys 1.18x

The ratio of total number of boys to girls = 1.18x : x = 1.18 : 1 = 59 : 50.

Hence, the correct option is (B).