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Calculation:

2(x + y) = 1  -------(1)

x - y = 3       -----------(2)

On multiplying equation(2) with 2 we get :

⇒ 2x - 2y = 6

On adding equation (1) and (2) :

2x + 2y + 2x - 2y = 7

4x = 7

x = 7/4

Putting value of x in eq(2) : 

7/4 - y = 3

y = - 5/4

∴ The correct answer is 7/4 , -5/4.

Given:

Sum of the cubes of two numbers in the ratio 5 ∶ 6 is 2728.

Calculation:

Let the number be 5x and 6x,

⇒ (5x)³ + (6x)³ = 2728

⇒ 125x³ + 216x³  = 2728

⇒ 341x³ = 2728

⇒ x³ = 8

⇒ x = 2

The sum of numbers = 5x + 6x = 11x = 22

∴ The correct answer is 22.

Given:

5 men and 7 women can do it in 10 days .

20 men and 42 women can do it in 2 days.

Formula used:

M₁H₁D₁/W₁ = M₂H₂D₂/W₂

Calculation:

According to question,

⇒ (5M + 7W) × 10 = (20M + 42W) × 2

⇒ 50M + 70W = 40M + 84W

⇒ 10M = 14W

⇒ M/W = 7/5

Total Work = (35 + 35) × 10 = 700

⇒ (10M + 15W) × x = 700

⇒ (70 + 75) × x = 700

⇒ x = 700/145 = 140/29

∴ The correct answer is 140/29.

Given:

The average of a non-zero number and its square is 8 times the number.

Concept used:

Average = Total ÷ Number of entities

Calculation:

Let the number be Q.

According to the question,

(Q + Q2)/2 = 8 × Q

⇒ Q2 + Q = 16Q

⇒ Q2 = 15Q

⇒ Q = 15 (∵ Q ≠ 0)

∴ The number is 15.

Calculation:

⇒ (62% of 720)/0.4

⇒ (62/100 × 720)/0.4

⇒ (62 × 7.2 × 10)/4

⇒ 1116

∴ The correct answer is 1116.

Calculation:

On simplifying further we get,

⇒ y² + 21/2y = 5

⇒ y² + 21 = 10y

⇒ y² - 10y + 21

⇒ y² - 3y - 7y + 21

⇒ y(y - 3) - 7(y - 3)

⇒ y = 3, 7

∴ The correct answer is 3 , 7.

Calculation:

Let two numbers be x & y, where x is larger.

x + y = 100                      ---(1)

According to the question -

⇒ x = 4y + 5                  ---(2)

Putting the value of (2) in (1)

⇒ 4y + 5 + y = 100

⇒ 5y + 5 = 100

⇒ y = 95/5 = 19

∴ The correct answer is 19.

Calculation:

\(\sqrt{361}=?-14^2-17\times 7 \)

19 = x - 196 - 119

x = 19 + 196 + 119

x = 334

∴ The correct answer is 334.

Calculation:

The expression \( \displaystyle\sum_{0}^{\infty} \dfrac{1}{2^n} \) represents an infinite series. To find the value of this series, we need to determine its formula and then evaluate it.

Note that the series starts at n=0 and each term is obtained by raising 1/2 to the power of n. Therefore, the formula for the series is:

\( \displaystyle\sum_{0}^{\infty} \dfrac{1}{2^n} \) = 1 + (1/2)¹ + (1/2)² + (1/2)³ + ...

This is a geometric series with first term a = 1 and common ratio r = 1/2. The formula for the sum of a geometric series is:

S = \(\dfrac{a}{(1 - r)}\)

Substituting the values of a and r, we get:

S = \(\dfrac{1}{(1 - \dfrac{1}{2})}\) = 2

∴ The volume of the cube is 2.

Given:

The average of five consecutive numbers is twenty.

Concept used:

We know the function of average is to balance out the numbers given.

If 4 is the average of 3 consecutive numbers then,

Numbers will be 3, 4, 5

Calculation:

According to the question average of 5 consecutive numbers is 20.

So the numbers will be,

⇒ 18, 19, 20, 21, 22

∴ The number starts with 18.

∴ The correct answer is 18.