CDS Elementary Mathematics 3

Question 1

Two pipes can fill a tank in 10 and 15 hours respectively. How long will they take together?

Accepted Answer

6 hours

Answer

Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6; time = 6 hours.

Question 2

If the ratio of two numbers is 3:5 and their sum is 96, what is the larger number?

Accepted Answer

60

Answer

Larger number = (5/8) × 96 = 60.

Question 3

A man walks 4 km north and then 3 km east. How far is he from his starting point?

Accepted Answer

5 km

Answer

Distance = √(4² + 3²) = √(16+9) = √25 = 5 km by the Pythagorean theorem.

Question 4

What is the compound interest on $1000 at 10% per annum for 2 years?

Accepted Answer

$210

Answer

CI = 1000 × (1.1)² − 1000 = 1210 − 1000 = $210.

Question 5

Solve: 3(2x − 4) = 18

Accepted Answer

x = 5

Answer

6x − 12 = 18 → 6x = 30 → x = 5.

CDS - Combined Defence Services