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intermediate25 min

Mixed Aptitude Problem Solving

Combining techniques from earlier lessons into realistic multi-step problems, plus honest, general advice for practicing under time pressure.

What you'll learn

  • Solve a multi-step word problem that combines a discount calculation with compound interest
  • Solve a multi-step word problem that combines time-and-work rates with a ratio-based split
  • Apply general estimation, elimination, and time-budgeting strategies when practicing timed problem sets

Prerequisites

Explanation

Real placement-test questions rarely test one technique in isolation — they string two or three together, and the biggest source of errors isn't any single calculation but losing track of which result feeds into which next step. This lesson is entirely about that skill: chaining earlier lessons' techniques correctly, in order.

Worked example (discount → compound interest). You buy furniture marked at ₹20,000. The store gives a 15% discount at checkout, and you pay the discounted price today by taking a loan at 10% annual compound interest for 2 years. How much do you owe at the end? Step one (discount lesson): selling price = 20,000 × (1 − 15/100) = 20,000 × 0.85 = ₹17,000. Step two (compound interest lesson): amount after 2 years = 17,000 × (1.10)² = 17,000 × 1.21 = ₹20,570. The key discipline here: the discounted price, not the marked price, is what earns interest — using the wrong intermediate value is the single most common way multi-step problems go wrong.

Worked example (time-and-work → ratio). Worker A can finish a job alone in 10 days, worker B in 15 days. They work together and split a ₹500 payment in proportion to how much work each contributed. How much does each receive? Step one (time-and-work lesson): their rates are 1/10 and 1/15. Step two (ratio lesson): simplify the rate ratio — common denominator 30 gives 3/30 : 2/30, i.e. a 3:2 ratio. Step three: split ₹500 in a 3:2 ratio (5 total parts, ₹100 each): A gets 3×100 = ₹300, B gets 2×100 = ₹200. The insight worth keeping: payment should be split by rate (work contributed), not by time taken — the faster worker did proportionally more of the job and fairly earns proportionally more.

On exam strategy. This platform is self-paced practice — it does not proctor, time-limit, or certify any official assessment, and nothing here is a substitute for whatever specific format a real placement test or exam actually uses. That said, a few honest, general habits tend to help whenever you do practice under a self-imposed time limit:

  • Estimate before you calculate precisely. A rough mental estimate (is the answer closer to 50 or 500?) instantly rules out wildly wrong multiple-choice options before you've done any real arithmetic.
  • Eliminate implausible choices first. If a discount problem's answer choices include a number larger than the original price, that choice can't be right — cross it out immediately.
  • Budget your time and move on if stuck. If you're well past what a question should reasonably take, mark it and continue — a skipped question costs you nothing you couldn't have lost by staring at it forever, and you can always come back, since this is untimed self-paced practice, not a proctored exam with a hard cutoff.

These are general, honest study habits — not claims about what any particular real exam allows or how it's graded.

Example

Combining a discount with compound interest requires feeding the discounted price forward as the new principal.

function loanRepaymentAfterDiscount(markedPrice, discountPercent, ratePercent, years) {
  const sellingPrice = markedPrice * (1 - discountPercent / 100);
  const amount = sellingPrice * Math.pow(1 + ratePercent / 100, years);
  return Math.round(amount * 100) / 100;
}
// Example: loanRepaymentAfterDiscount(20000, 15, 10, 2) -> 20570

Guided exercise

Guided exercise

Write discountThenCompoundAmount(markedPrice, discountPercent, ratePercent, years) that first applies a single percentage discount to markedPrice to get a selling price, then grows that selling price using annual compound interest at ratePercent for the given years. Return the final amount rounded to 2 decimal places.

Checks: Combines a discount with two years of compounding · Combines a discount with one year of compounding · plus 1 hidden check

Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.

Loading editor…

Stuck? Get a hint.

Independent exercise

Independent exercise

Write shareOfPaymentByWorkRatio(daysList, totalPayment) where daysList gives the number of days each of several workers would take to finish a job alone. The workers complete the job together and split totalPayment in proportion to their individual work rates (1/days). Return an array of each worker's share, in the same order as daysList, each rounded to 2 decimal places.

Checks: Splits payment between two workers with different rates · Splits payment evenly between two equally-paced workers · plus 1 hidden check

Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.

Loading editor…

Stuck? Get a hint.

Common mistakes

  • Applying a later step's formula to the original starting value instead of the previous step's result (for example, compounding the marked price instead of the discounted price).
  • Spending disproportionate time on one difficult multi-step question during timed practice instead of budgeting time and returning to it later.
  • Mistaking self-paced practice on this platform for an official, proctored, or certifying assessment -- it isn't, and no score here should be treated as equivalent to a real exam result.

Knowledge check

Knowledge check

1. A retailer buys a gadget for ₹4,000, marks it up by 25% to set the marked price, then offers a 10% discount at checkout. What is the retailer's actual profit percentage, based on the original cost price?
2. When practicing timed problem sets on this platform and you get stuck on one question, which approach is most reasonable?
3. Worker A can complete a task alone in 20 days. Worker B is 25% more efficient than A. How many days will B alone take to complete the same task?

Takeaway

Multi-step problems reward carefully tracking which result feeds into the next step far more than they reward speed on any single formula.

Summary

Combining techniques -- like discount feeding into compound interest, or work rates feeding into a ratio-based payment split -- is mostly about correctly chaining intermediate results rather than learning any new formula. Practicing on this platform is self-paced and untimed by design, so honest general strategies like estimating, eliminating implausible choices, and budgeting time across questions are worth building as habits, understanding that this is practice, not a proctored or certifying exam.

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