If a sum of ₹5,000 is taken at a simple rate of interest of 15% per annum for 3 years and another sum of ₹8,000 is taken at a simple interest of 12% per annum for 4 years, the positive difference of the interests paid is:
- (a)₹1,286
- (b)₹1,378
- (c)₹1,643
- (d)₹1,590
Answer
Why
Correct — D. Simple interest is P × R × T ⁄ 100, and the two sums are independent, so compute each one fully before subtracting.
First sum: 5,000 × 15 × 3 ⁄ 100 = ₹2,250
Second sum: 8,000 × 12 × 4 ⁄ 100 = ₹3,840
Positive difference = 3,840 − 2,250 = ₹1,590 → option (d)
Working per year is quicker and safer with these zeros: ₹5,000 at 15% earns ₹750 a year, so ₹2,250 over three years; ₹8,000 at 12% earns ₹960 a year, so ₹3,840 over four.
Why the others are wrong
- (a)₹1,286 — ₹1,286 is not a multiple of 30, so it cannot be this gap: 30 × 42 = 1,260 and 30 × 43 = 1,290. Both yearly interests, ₹750 and ₹960, are multiples of 30, so their difference must be too.
- (b)₹1,378 — ₹1,378 leaves a remainder of 28 on division by 30, so the same divisibility test rules it out.
- (c)₹1,643 — ₹1,643 is odd, but both interests here are even — ₹2,250 and ₹3,840 — so their difference has to be even, and this one goes without finishing the arithmetic.
Concept
Simple interest is charged on the original principal only, never on interest already earned, so it stays flat at P × R × T ⁄ 100 for the whole term.
That makes the per-year figure the useful unit: a principal P at R% earns PR⁄100 every single year, and the term merely multiplies it.
Two separate loans are two independent calculations — nothing about the first touches the second. The contrast with compound interest is worth carrying: ₹5,000 at 15% for three years earns ₹2,250 simple, but about ₹2,604 compounded annually.
'Positive difference' only instructs you to subtract the smaller from the larger; it adds no arithmetic.
None of the three wrong options corresponds to a recognisable slip, so there is no shortcut by guessing the intended error — but the divisibility check on 30 disposes of all three quickly.
Key facts
- Simple interest = P × R × T ⁄ 100, on the original principal for the full term.
- ₹5,000 at 15% simple interest earns ₹750 per year, so ₹2,250 in three years.
- ₹8,000 at 12% simple interest earns ₹960 per year, so ₹3,840 in four years.
- The positive difference of those two interests is ₹1,590.
Study next
Common traps
- Applying one time period to both sums — the terms here are three years and four years.
- Adding the two interests instead of subtracting, which gives ₹6,090.
- Dropping a zero while dividing 5,000 × 15 × 3 by 100.
SSC pairs two independent deposits and asks for the sum, the difference or the ratio of their interests. The numbers are always chosen so both interests come out in whole rupees, which is itself a check on your arithmetic.
Related PYQs
No directly related past PYQ was found.