Explanation

Given:

$$X : Y = 3 : 4 quad text{and} quad Y : Z = 5 : 8$$

Step 1: Make Y common

• From $X:Y=3:4$, let$X=3k$, $Y = 4k$

• From $Y:Z = 5:8$, let $Y = 5m$, $Z=8m$

Step 2: Equate Y

$$4k = 5m implies k = frac{5}{4} m$$

Then:

$$X = 3k = 3 cdot frac{5}{4} m = frac{15}{4} m$$ $$Y = 4k = 5m$$$$Z = 8m$$

Step 3: Compute the expression

$$frac{2Y}{3X - Y + 2Z} = frac{2 cdot 5m}{3 cdot frac{15}{4} m - 5m + 2 cdot 8 m}$$3X−Y+2Z​=2⋅5m/ 3⋅15​/4m−5m+2⋅8m​

Numerator: $2\cdot 5m=10m$

Denominator:

3⋅15/4​m=45​/4m
45/4​m−5m+16m=45/4​m−20​/4m+64/4​m=89/4​m$$frac{2Y}{3X - Y + 2Z} = frac{10 m}{frac{89}{4} m} = frac{10 cdot 4}{89} = frac{40}{89}$$3X−Y+2Z​=10m​/89/4=10⋅4/89​=40/89​

Explanation

Explanation

Step-by-step Solution:

Given numbers:

17, 13, 18, 17, 14, 18, 19, 17, 13, 16, 18, 20

1. Arrange in ascending order:

13, 13, 14, 16, 17, 17, 17, 18, 18, 18, 19, 20

2. Count the numbers:

Total = 12 (even number)

3. Median = average of the 6th and 7th terms:

6th term = 17, 7th term = 17

Median = (17 + 17) / 2 = 17

Explanation

x + y = 67 ... (equation 1)

x - y = 3 ... (equation 2)

where x and y are the two numbers.

We can solve this system of equations by adding equation 1 and equation 2, which eliminates y:

2x = 70

Dividing both sides by 2 gives:

x = 35

Now that we have x, we can substitute it into equation 1 to find y:

35 + y = 67

Subtracting 35 from both sides gives:

y = 32

So, the two numbers are 35 and 32.

Explanation

To calculate Ali's intelligence quotient (IQ), we use the formula:

IQ = (Mental Age / Chronological Age) * 100

Given that Ali's mental age is 12 and his chronological age is 10:

IQ = (12 / 10) * 100

= 1.2 * 100

= 120