CUET UG 2025 — General Test Arithmetic

Let the original principal amount be $P$P.

When the money becomes 3-fold at 4% annual rate:

Final Amount $= 3P$=3P

Interest Earned $= 3P - P$=3P−P

Interest Earned $= 2P$=2P

Using the simple interest formula where Rate $= 4\%$=4% and Time $= T$=T years:

$$\text{Interest} = \dfrac{P \times R \times T}{100}$$Interest=100P×R×T​

$$2P = \dfrac{P \times 4 \times T}{100}$$2P=100P×4×T​

$$2 = \dfrac{4T}{100}$$2=1004T​

$$200 = 4T$$200=4T

$T = 50$T=50 years

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For the money to become 6-fold in the same time period of 50 years:

Final Amount $= 6P$=6P

Interest Earned $= 6P - P$=6P−P

Interest Earned $= 5P$=5P

Let the required rate be $R\%$R%.

$$5P = \dfrac{P \times R \times 50}{100}$$5P=100P×R×50​

$$5 = \dfrac{50R}{100}$$5=10050R​

$$500 = 50R$$500=50R

$$R = 10\%$$R=10%

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Therefore, the rate of interest required for the sum to become 6-fold is $10\%$10%.