Question:
Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?
Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?
Updated On: Jul 25, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
We use the formula for Simple Interest:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Step 1: Calculate yearly interest for both
Veeru's yearly interest: \[ = \frac{10000 \times 5 \times 1}{100} = ₹500 \]
Joy's yearly interest: \[ = \frac{8000 \times 10 \times 1}{100} = ₹800 \]
Step 2: Determine the difference
- Difference in yearly interest = ₹800 - ₹500 = ₹300
- Veeru invested for 2 years initially → Interest earned = ₹500 × 2 = ₹1000
- Difference in principal = ₹10000 - ₹8000 = ₹2000
- Total difference (to match Joy) = ₹1000 (interest gap) + ₹2000 (principal gap) = ₹3000
Step 3: Time to cover the ₹3000 gap
\[ \text{Time} = \frac{₹3000}{₹300 \text{ per year}} = 10 \text{ years} \]
Final Answer:
Veeru has already invested for 2 years. To match Joy’s total, he must invest for:
\[ 2 + 10 = \boxed{12 \text{ years}} \]
Was this answer helpful?
0
0
Top Questions on SI & CI
- Ramesh bought a mobile from a local store. He paid 1/6 of the price via UPI and 1/3 of the price via cash. He agreed to pay the balance amount a year later. While paying back the balance amount, Ramesh paid 10% interest on the balance amount. If the interest paid was Rs. 6000, what was the original price of the mobile?
- A sum of money triples itself in 8 years at simple interest. In how many years will it become five times itself at the same rate?
- ₹ 45000 is deposited at compound interest for 4 years. The rates are 6% (1st year), then increase by 1% each year (so 7%, 8%, 9%). Find the approximate amount at the end of 4 years.
- On a certain principal, CI and SI at a certain rate of interest for 2 years is ₹ 16560 and ₹ 14400 respectively. Find the principal and rate of interest per annum.
- Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
View More Questions
Questions Asked in CAT exam
When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?
- CAT - 2024
- Algebra
- A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
- CAT - 2024
- Mensuration
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
- Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
- CAT - 2024
- Time and Work
View More Questions