Rishi has ₹1,612 with him. He divided it amongst his sons Shan and Piyush and asked them to invest it at 8% rate of interest per annum, compounded annually. It was seen that Shan and Piyush got the same amount after 19 and 20 years, respectively. How much (in ₹) did Rishi give to Shan?

775

875

687

837

APEDIA

RRB NTPC Graduate Tier 1

2025 • 09 Jun, 2025 • Shift-1

Rishi has ₹1,612 with him. He divided it amongst his sons Shan and Piyush and asked them to invest it at 8% rate of interest per annum, compounded annually. It was seen that Shan and Piyush got the same amount after 19 and 20 years, respectively. How much (in ₹) did Rishi give to Shan?

Correct Answer

837

Investment Allocation Logic: Let the principal amount given to Shan be 'S' and to Piyush be 'P'. The total sum is S + P = 1612.Compound Interest Equivalence: Th......

💡 Analysis & Explanation

Investment Allocation Logic ▼

Let the principal amount given to Shan be 'S' and to Piyush be 'P'. The total sum is S + P = 1612.

Compound Interest Equivalence ▼

The final amount is calculated using the compound interest formula. We are given that S * (1 + 8/100)^19 = P * (1 + 8/100)^20.

Ratio Derivation ▼

Simplifying the equation by dividing both sides by the 19th power of the growth factor yields S = P * (1 + 8/100). This simplifies to S = P * (108/100) = P * (27/25). Therefore, the proportional ratio of S to P is 27:25.

Final Share Calculation ▼

The total ratio parts equal 27 + 25 = 52 parts. The monetary value of one part is 1612 / 52 = 31. Shan's share (S) corresponds to 27 parts, so 27 * 31 = 837.

Conclusion ▼

Shan received a principal amount of ₹837.

Choose Language

See you soon!

Rishi has ₹1,612 with him. He divided it amongst his sons Shan and Piyush and asked them to invest it at 8% rate of interest per annum, compounded annually. It was seen that Shan and Piyush got the same amount after 19 and 20 years, respectively. How much (in ₹) did Rishi give to Shan?