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