SSC CGL 2024 Tier-I · 24 September 2024, Shift 2 · Quantitative Aptitude · Question 18 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

A cell phone is available for Rs.600 or for Rs.300 cash down payment together with Rs.360 to be paid after two months. Find the rate of interest charged under this scheme.

(a)60%
(b)20%
(c)120%
(d)50%

Answer

Why

Correct — C. Paying cash costs Rs.600. Under the scheme you hand over Rs.300 now, so Rs.300 of the price is still owed — and that unpaid balance is the principal.

Principal P = 600 − 300 = Rs.300
Amount paid two months later = Rs.360
Interest = 360 − 300 = Rs.60

Time T = 2 months = 2⁄12 = 1⁄6 year
R = (SI × 100) ⁄ (P × T) = (60 × 100) ⁄ (300 × 1⁄6)

= 6000 ⁄ 50 = 120% per annum → option (c)

Why the others are wrong

(a)
60% — 60% comes from using the full Rs.600 as the principal: 60⁄600 = 10% over two months, times 6 gives 60%. But Rs.300 was already paid in cash, so only Rs.300 is on loan. At 60% the deferred payment would be Rs.330, not Rs.360.
(b)
20% — 20% is the two-month rate, not the annual one. 60⁄300 = 20% is the charge for the period, and simple interest is always quoted per annum, so it still has to be multiplied by 6. At 20% a year the deferred payment would be Rs.310.
(d)
50% — At 50% per annum the interest on Rs.300 for two months is 300 × 0.50 × 1⁄6 = Rs.25, making the deferred payment Rs.325. The paper fixes it at Rs.360, so 50% is too low.

Concept

This is the hire-purchase form of simple interest. The same article carries a cash price and an instalment price, and the gap between them is interest on whatever is left unpaid.

Two decisions settle the sum. The principal is the unpaid balance, not the full price — Rs.600 − Rs.300 = Rs.300 here.

And the rate is per annum, so a two-month gap enters the formula as 1⁄6 of a year. Miss either and the arithmetic is clean but the answer is out by a factor of 2 or of 6.

The rate looks absurd until you notice the scale: Rs.60 of interest on Rs.300 held for only two months. Annualising a small, short loan produces a large percentage, so do not reject 120% as impossible — recheck the arithmetic instead.

Key facts

In a hire-purchase sum the principal is the cash price minus the cash down payment, here Rs.600 − Rs.300 = Rs.300.
The interest charged is Rs.360 − Rs.300 = Rs.60, for a period of two months.
Simple interest rates are quoted per annum, so two months enters the formula as 2⁄12 = 1⁄6 year.
R = (SI × 100) ⁄ (P × T) gives (60 × 100) ⁄ (300 × 1⁄6) = 120%.

Study next

Simple interest: finding the rate when principal, interest and time are all givenInstalment sums where a debt is discharged by equal annual paymentsConverting months and days into years inside the SI formula

Common traps

Using Rs.600 as the principal instead of the Rs.300 still owed.
Stopping at 20%, which is the charge over two months rather than the annual rate.
Writing T = 2 instead of T = 2⁄12 in the formula.

SSC sets deferred-payment interest as a short, self-contained arithmetic item. A debt of Rs.26,160 discharged by equal annual instalments at 6% simple interest is asked on 10 Sep 2024, 12:30, Quant Q.19.

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