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

Explanation

aₙ = a + (n - 1)d

Let a be the first term, d the common difference.

Given:  

2nd term: a + d = 20  

8th term: a + 7d = 60

Subtract the two equations:  

(a + 7d) - (a + d) = 60 - 20  

6d = 40 ⇒ d = 40 / 6 = 20 / 3

Now plug d = 20/3 into a + d = 20:  

a = 20 - 20/3 = (60 - 20)/3 = 40/3

Now find the 20th term:  

a + 19d = 40/3 + 19 × (20/3) = (40 + 380)/3 = 420/3 = 140

Explanation

Let the two numbers be 3x and 4x.

LCM of 3x and 4x = LCM(3,4) × x = 12x

We’re given that:  

12x = 240 ⇒ x = 20

So, the two numbers are:  

3x = 60 and 4x = 80

Smaller number = 60

Explanation

Given:

- Q is as much younger than R as he is older than T  

  ⇒ R - Q = Q - T  

  ⇒ Rearranged: R + T = 2Q ...(1)

Also given:

- R + T = 50 ...(2)

From (1) and (2):  

2Q = 50 ⇒ Q = 25

Now put Q = 25 into equation:  

R + T = 50  

So, we still don’t know individual values of R or T, but we can find difference between R and Q:

From earlier:  

R - Q = Q - T  

⇒ R - 25 = 25 - T  

⇒ R + T = 50 (same again)

Now solve:  

R - 25 = 25 - T  

Add both sides:  

R - 25 + T = 25  

⇒ R + T = 50 

So we get consistent results.

Now, what is R - Q?  

Let’s find R:  

From earlier:

R - 25 = 25 - T ⇒ R = 50 - T

Now R - Q = R - 25 = (50 - T) - 25 = 25 - T

So unless T is given, we can’t determine exact value of R - Q

Correct Answer: D) Data inadequate 

Explanation

Step 1: Divide 2460 by 6  

2460 ÷ 6 = 410 km

Explanation

Time at original speed = 240 / x  

Time at increased speed = 240 / (x + 4)  

Given:  

240/x - 240/(x + 4) = 0.5

Multiply through by x(x + 4) to eliminate denominators:

240(x + 4) - 240x = 0.5x(x + 4)  

240x + 960 - 240x = 0.5x² + 2x  

960 = 0.5x² + 2x  

Multiply both sides by 2:  

1920 = x² + 4x  

x² + 4x - 1920 = 0

Solve the quadratic:  

x² + 4x - 1920 = 0  

Using quadratic formula:  

x = [-4 ± √(16 + 7680)] / 2  

x = [-4 ± √7696] / 2  

√7696 ≈ 87.7  

x ≈ (-4 + 87.7)/2 ≈ 83.7/2 ≈ 41.85

Approximate correct option is 40 km/h

Explanation

We are given:

- 3rd term = 8  

- 6th term = 17  

- We need to find the 8th term.

Formula for nth term of an AP:  

Tₙ = a + (n - 1)d

Let’s form equations:

1) T₃ = a + 2d = 8  

2) T₆ = a + 5d = 17  

Subtract (1) from (2):  

(a + 5d) - (a + 2d) = 17 - 8  

⇒ 3d = 9  

⇒ d = 3  

Now plug back to find a:  

a + 2(3) = 8  

⇒ a + 6 = 8  

⇒ a = 2

Now find the 8th term:  

T₈ = a + 7d = 2 + 7(3) = 2 + 21 = 23