Rakesh invests a sum of ₹5,000 and Shivam invests a sum of ₹9,000 at the same rate of simple interest per annum. If, at the end of 3 years, Shivam gets ₹360 more interest than Rakesh, then find the rate of interest per annum (in percentage).

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RRB NTPC Graduate Tier 1

2025 • 09 Jun, 2025 • Shift-1

Rakesh invests a sum of ₹5,000 and Shivam invests a sum of ₹9,000 at the same rate of simple interest per annum. If, at the end of 3 years, Shivam gets ₹360 more interest than Rakesh, then find the rate of interest per annum (in percentage).

Correct Answer

Formulaic Setup: The universal formula for Simple Interest is (Principal × Rate × Time) / 100. Let the unknown uniform rate of interest be R%. Both ......

💡 Analysis & Explanation

Formulaic Setup ▼

The universal formula for Simple Interest is (Principal × Rate × Time) / 100. Let the unknown uniform rate of interest be R%. Both investments are kept for an identical timeframe of 3 years.

Differential Analysis ▼

Shivam's total accumulated interest is (9000 × R × 3) / 100 = 270R. Rakesh's total accumulated interest is (5000 × R × 3) / 100 = 150R.

Equating the Difference ▼

The problem explicitly states that the gap between their earned interests is strictly ₹360. Constructing the equation gives: 270R - 150R = 360.

Solving for the Variable ▼

Simplifying the left side yields 120R = 360. Dividing both sides by 120 isolates the variable, giving R = 3.

Conclusion ▼

The uniformly applied annual rate of interest is exactly 3%.

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Rakesh invests a sum of ₹5,000 and Shivam invests a sum of ₹9,000 at the same rate of simple interest per annum. If, at the end of 3 years, Shivam gets ₹360 more interest than Rakesh, then find the rate of interest per annum (in percentage).