A sum of money gets doubled in 5 years at X% simple interest. If the interest was Y%, the sum of money would have become ten-fold in thirty years. What is Y - X (in t)

Option a: 10. Solution: Derivation of Difference in Simple Interest Rates Given: - Scenario 1: Sum doubles in 5 years at X% simple interest. - Scenario 2: Sum becomes 10-fold (A = 10P) in 30 years at Y% simple interest. Step 1: Solve for X If the sum doubles, simple interest earned equals principal (SI1 = P). P = P x X x 5/100 implies 1 = 5 X/100 implies X = 20% Step 2: Solve for Y If the sum becomes 10-fold, simple interest earned is 9P (SI2 = 10P - P = 9P). 9P = P x Y x 30/100 implies 9 = 30 Y/100 implies Y = 30% Step 3: Calculate Y - X Y - X = 30% - 20% = 10% Hence, Option A is the correct answer.

A sum of money gets doubled in $5$ years at $X\%$ simple interest. If the interest was $Y\%$, the sum of money would have become ten-fold in thirty years. What is $Y - X$ (in $t$)

The correct answer is Option a: $10$. **Derivation of Difference in Simple Interest Rates** Given: - Scenario 1: Sum doubles in $5$ years at $X\%$ simple interest. - Scenario 2: Sum becomes 10-fold ($A = 10P$) in $30$ years at $Y\%$ simple interest. **Step 1: Solve for $X$** If the sum doubles, simple interest earned equals principal ($SI_1 = P$). $$P = \frac{P \times X \times 5}{100} \implies 1 = \frac{5 X}{100} \implies X = 20\%$$ **Step 2: Solve for $Y$** If the sum becomes 10-fold, simple interest earned is $9P$ ($SI_2 = 10P - P = 9P$). $$9P = \frac{P \times Y \times 30}{100} \implies 9 = \frac{30 Y}{100} \implies Y = 30\%$$ **Step 3: Calculate $Y - X$** $$Y - X = 30\% - 20\% = 10\%$$ Hence, **Option A** is the correct answer.

Mathematics for FinanceMTP Oct 21Question 1338 of 512

All Questions

A sum of money gets doubled in $\displaystyle 5$ years at $\displaystyle X\%$ simple interest. If the interest was $\displaystyle Y\%$ , the sum of money would have become ten-fold in thirty years. What is $\displaystyle Y - X$ (in $\displaystyle t$ )

Options

\displaystyle 10

\displaystyle 5

\displaystyle 8

Dnone of these

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Correct Answer

✅ Option a — $\displaystyle 10$

All Options:

A $\displaystyle 10$
B $\displaystyle 5$
C $\displaystyle 8$
Dnone of these

Detailed Solution & Explanation

**Derivation of Difference in Simple Interest Rates** Given: - Scenario 1: Sum doubles in

\displaystyle 5

years at

\displaystyle X\%

simple interest. - Scenario 2: Sum becomes 10-fold (

\displaystyle A = 10P

) in

\displaystyle 30

years at

\displaystyle Y\%

simple interest. **Step 1: Solve for

\displaystyle X

** If the sum doubles, simple interest earned equals principal (

\displaystyle SI_1 = P

P = \frac{P \times X \times 5}{100} \implies 1 = \frac{5 X}{100} \implies X = 20\%

**Step 2: Solve for

\displaystyle Y

** If the sum becomes 10-fold, simple interest earned is

\displaystyle 9P

(

\displaystyle SI_2 = 10P - P = 9P

9P = \frac{P \times Y \times 30}{100} \implies 9 = \frac{30 Y}{100} \implies Y = 30\%

**Step 3: Calculate

\displaystyle Y - X

Y - X = 30\% - 20\% = 10\%

Hence, **Option A** is the correct answer.

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A sum of money gets doubled in 5\displaystyle 55 years at X%\displaystyle X\%X% simple interest. If the interest was Y%\displaystyle Y\%Y%, the sum of money would have become ten-fold in thirty years. What is Y−X\displaystyle Y - XY−X (in t\displaystyle tt)