CUET PG 2023 — Reasoning PYQ

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Question

CUET PG 2023 — Reasoning PYQ

CUET PG | Reasoning | 2023

A sum of money doubles itself on simple interest in 10 years. Find the rate of interest per annum.

Choose the correct answer:

Explanation

Step 1: Define the Variables

Let:

$P$ = Principal amount
$R$ = Rate of interest per annum
$T$ = Time in years = $10\text{ years}$
$A$ = Amount after 10 years

According to the question, the sum of money doubles itself:

A = 2P

Step 2: Calculate Simple Interest ( $SI$ )

The Simple Interest is the difference between the Amount and the Principal:

SI = A - P

SI = 2P - P = P

Step 3: Apply the Simple Interest Formula

The formula for Simple Interest is:

SI = \frac{P \times R \times T}{100}

Substitute the values $SI = P$ and $T = 10$ :

P = \frac{P \times R \times 10}{100}

Step 4: Solve for $R$

Divide both sides by $P$ :

1 = \frac{R \times 10}{100}

1 = \frac{R}{10}

R = 10\%

Final Answer

The rate of interest per annum is $10\%$ .