Explanation

First 10 prime numbers are:  

2, 3, 5, 7, 11, 13, 17, 19, 23, 29  

Sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129  

Arithmetic mean = Sum / Number of terms  

= 129 / 10  

= 12.9  

Last verified on 26-07-2026

Explanation

Given A:B = 3:4 and B:C = 12:13.

First, make the ratios for B consistent:

A:B = 3:4 = 9:12 (multiplied by 3)

Now, B:C = 12:13

A:B:C = 9:12:13

A:C = 9:13

Last verified on 17-06-2026

Explanation

Explanation

Explanation

(2x + y) + (x − y) = 11 + 1

3x = 12

x = 4

Last verified on 13-05-2026

Explanation

3x − 4 = 17

3x = 17 + 4 = 21

x = 21 ÷ 3 = 7

Last verified on 13-05-2026

Explanation

Time for first part = 60 ÷ 40 = 1.5 h

Time for return = 60 ÷ 60 = 1 h

Total distance = 120 km

Total time = 2.5 h

Average speed = 120 ÷ 2.5 = 48 km/h

Last verified on 13-05-2026

Explanation

In 12 L mixture with ratio 1:3:  

Total parts = 1 + 3 = 4  

Water = (1/4) × 12 = 3 L  

Milk = (3/4) × 12 = 9 L  

Let x liters of water be added. Milk stays 9 L.  

New ratio: (3 + x) : 9 = 2 : 3  

So (3 + x)/9 = 2/3  

3(3 + x) = 18  

9 + 3x = 18  

3x = 9  

x = 3  

Last verified on 13-05-2026

Explanation

Let A = 3x, B = 5x

Increase B by 20% → new B = 5x × 1.2 = 6x

New ratio = A : B = 3x : 6x = 3 : 6 = 1 : 2

Last verified on 12-05-2026

Explanation

7 parts = 14 km → 1 part = 2 km

9 parts = 9 × 2 = 18 km

So second distance = 18 km

Last verified on 12-05-2026