A car with a price of ₹6,50,000 is bought by making some down payment. On the balance, a simple interest of 10% is charged in lump sum and the money is to be paid in 20 equal annual instalments of ₹25,000. How much is the down payment?

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SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 2)
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  1. ₹1,55,945
  2. ₹1,95,455
  3. ₹1,94,555
  4. ₹1,45,955

Answer (Detailed Solution Below)

Option 2 : ₹1,95,455
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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Given:

A car with a price of ₹6,50,000 is bought by making some down payment. On the balance, a simple interest of 10% is charged in lump sum and the money is to be paid in 20 equal annual instalments of ₹25,000. 

Concept used:

Amount becomes in lump sum = P(1 + R%)

P = Principal

R = Rate of interest

Calculation:

Let the downpayment be of Rs. X.

​According to the question,

(650000 - X) × (1 + 10%) = 25000 × 20

⇒ (650000 - X) × (1 + 10%) = 500000

⇒ (650000 - X) = 500000 ÷ (1 + 10%)

⇒ (650000 - X) ≈ 454545.45

⇒ X ≈ 650000 - 454545

⇒ X ≈ 195455

∴ The downpayment was Rs. 195455.

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