Explanation

From "BOY" = 539  

So:  

- B = 5  

- O = 3  

- Y = 9  

From "GIRL" = 8627  

So:  

- G = 8  

- I = 6  

- R = 2  

- L = 7  

Now code GLORY using these values:  

- G = 8  

- L = 7  

- O = 3  

- R = 2  

- Y = 9  

So, GLORY = 87329

Explanation

 The letter E appears once in the word "tea"  

- It appears twice in "coffee"  

- It does not appear in "milk."  

So, the riddle is about letters, not actual ingredients.

Explanation

Semi was 21 years old in 1945.

The number of years from 1945 to 1965 is 20 years.

21 + 20 = 41

Explanation

Raza is ranked ninth from the top. That means there are 8 students above Raza.

Raza is 38th from the bottom. That means there are 37 students below him.

So total students 8 + Raza + 37 = 46 students

Explanation

The word ARTICLE has 7 letters:  

A, R, T, I, C, L, E  

Vowels = A, I, E (3 vowels)  

Consonants = R, T, C, L (4 consonants)  

Even positions in a 7-letter word: 2, 4, 6 → 3 even positions  

Step 1:

Place vowels in even positions  

We have 3 vowels and 3 even positions  

→ Number of ways = 3! = 6

Step 2:

Place consonants in the remaining 4 positions  

→ Number of ways = 4! = 24

Step 3:

Total number of words = 3! × 4! = 6 × 24 = 144

Explanation

We are given:

(x - 3)(x - 4) = 1

Step 1: Expand the left-hand side:

(x - 3)(x - 4) = x² - 7x + 12

So the equation becomes:

x² - 7x + 12 = 1

Step 2: Bring all terms to one side:

x² - 7x + 11 = 0

Step 3: Use the quadratic formula:

x = [7 ± √(49 - 44)] / 2  

x = [7 ± √5] / 2

Final Answer:

x = (7 ± √5)/2

Explanation

Divisible by 2 → Yes

Divisible by 5 → Yes

Divisible by 10 → Yes

So 3200 is divisible by 2, 5, and 10.

Explanation

Let two numbers be 4x and 5x

Their LCM = 180 and HCF = x

Now,

1st number × 2nd number = LCM × HCF

Or, 4x × 5x = 180 × x

Or, 20x = 180

Or, x = 9

Then, the smaller number = 4 × 9 = 36

Explanation

Given:

- Ratio of ages of A and B = 6 : 5  

- After 5 years, ratio = 9 : 8  

Let the ages be:

A = 6x  

B = 5x  

After 5 years:

(A + 5) / (B + 5) = 9 / 8

=> (6x + 5) / (5x + 5) = 9 / 8

Cross multiply:

8(6x + 5) = 9(5x + 5)  

48x + 40 = 45x + 45  

48x - 45x = 45 - 40  

3x = 5  

x = 5 / 3

Age difference = A - B = 6x - 5x = x = 5/3 years

Explanation

Work done by A per hour = 1/(6*7) = 1/42  

Work done by B per hour = 1/(8*7) = 1/56  

Combined work per hour = 1/42 + 1/56 = (4/168 + 3/168) = 7/168 = 1/24

At 8 hours/day, work per day = 8 * 1/24 = 1/3

Total days to complete = 1 / (1/3) = 3 days