Question

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. Rs. 110000
• B. Rs. 150000
• C. Rs. 120000
• D. Rs. 100000
• E. Rs. 90000

Hint:

When dealing with interest calculations, make sure to correctly identify the principal amount and apply the interest rate to the correct amount.

Answer 1

The Correct Option is C

To find the original price of the mobile, let's follow the problem step by step. 

1. Let's assume the original price of the mobile is \(P\).
2. Ramesh paid \(\frac{1}{6}\) of the price via UPI and \(\frac{1}{3}\) of the price via cash.
3. The total amount paid initially is: \(P \times \left(\frac{1}{6} + \frac{1}{3}\right) = P \times \left(\frac{1}{6} + \frac{2}{6}\right) = P \times \frac{3}{6} = \frac{P}{2}\).
4. This implies that the remaining amount to be paid after one year is: \(P - \frac{P}{2} = \frac{P}{2}\).
5. Ramesh agreed to pay 10% interest on this remaining amount after one year.
6. The interest paid on the balance is Rs. 6000.
7. The interest on the balance can be calculated as: \(\frac{10}{100} \times \frac{P}{2} = 6000\).
8. Simplifying the above equation: \(\frac{5P}{100} = 6000\)
9. Solving for \(P\): \(P = \frac{6000 \times 100}{5} = 120000\).

Thus, the original price of the mobile is Rs. 120000.

Looking at the options provided, the correct answer is Rs. 120000.

Answer 2

Step 1: Calculate the balance amount.
Let the original price of the mobile be \( x \). - He paid 1/6 of the price via UPI: \[ \text{UPI payment} = \frac{x}{6} \] - He paid 1/3 of the price via cash: \[ \text{Cash payment} = \frac{x}{3} \] So, the total amount paid so far is: \[ \frac{x}{6} + \frac{x}{3} = \frac{x}{6} + \frac{2x}{6} = \frac{3x}{6} = \frac{x}{2} \] Hence, the balance amount that Ramesh still owes is: \[ \text{Balance amount} = x - \frac{x}{2} = \frac{x}{2} \]
Step 2: Calculate the interest.
Ramesh paid 10% interest on the balance amount. The interest paid is given as Rs. 6000: \[ \text{Interest} = 10% \times \frac{x}{2} = \frac{10}{100} \times \frac{x}{2} = \frac{x}{20} \] We are given that the interest paid is Rs. 6000: \[ \frac{x}{20} = 6000 \]
Step 3: Solve for \( x \).
Multiplying both sides by 20: \[ x = 6000 \times 20 = 120000 \]
Final Answer: \[ \boxed{\text{Rs. 120000}} \]