Shawn invested one half of his total savings in a bond that paid simple interest for 2 years and received Rs. 550 as interest. He invested the remaining half in another bond that paid compound interest, compounded annually for the same 2 years and at the same rate of interest, and received Rs. 605 as interest. What was the value of his total savings before investing in these two bonds?

Introduction:
This is a mixed simple interest and compound interest problem, where the same rate is used in both parts. Shawn splits his savings into two equal halves and earns different interest amounts because of the difference in how interest is calculated. The objective is to find his original total savings by forming and solving equations.

Given Data / Assumptions:
Total savings = S (unknown). First half invested in simple interest for 2 years gives interest = Rs. 550. Second half invested in compound interest for 2 years gives interest = Rs. 605. Rate of interest r% per annum is the same for both bonds, and CI is compounded annually.

Concept / Approach:
Let each half be S/2. For the simple interest investment: SI = (S/2) * r * 2 / 100 = S * r / 100 = 550. From this, we can express S in terms of r. For the compound interest half, we use: CI = (S/2) * [(1 + r/100)^2 − 1] = 605. By substituting S from the first relation into the second, r can be found, and then S can be determined.

Step-by-Step Solution:
Step 1: From the simple interest part. S * r / 100 = 550 ⇒ S * r = 55,000. So S = 55000 / r. Step 2: From the compound interest part. Principal for CI = S/2. CI for 2 years = (S/2) * [(1 + r/100)^2 − 1] = 605. Expand (1 + r/100)^2 − 1 = 2r/100 + (r/100)^2. This equals r(200 + r) / 10000. So 605 = (S/2) * r(200 + r) / 10000. Substitute S = 55000 / r to eliminate S. 605 = (55000 / (2r)) * r(200 + r) / 10000 = 27500 * (200 + r) / 10000. So 605 = 2.75 * (200 + r). 200 + r = 605 / 2.75 = 220 ⇒ r = 20%. Step 3: Find S. S = 55000 / 20 = Rs. 2,750.

Verification / Alternative check:
Simple interest on S/2 = 2750/2 = 1,375 at 20% for 2 years: SI = 1375 * 20 * 2 / 100 = 1375 * 0.4 = Rs. 550. Compound interest on 1,375 at 20% for 2 years: Amount = 1375 * (1.2)^2 = 1375 * 1.44 = Rs. 1,980. CI = 1980 − 1375 = Rs. 605. Both match the given values, confirming S = 2,750.

Why Other Options Are Wrong:
All other options produce either wrong simple interest or wrong compound interest when substituted back, because they do not satisfy both conditions simultaneously for a single consistent rate.

Common Pitfalls:
The most common error is to treat the two halves independently without linking them through the same rate, or to fail to eliminate r properly. Some learners also misexpand (1 + r/100)^2. Keeping track of algebraic expressions step by step is crucial.

Final Answer:
Shawn's total savings before investing in the two bonds were Rs. 2,750.