Quick answers: (1) 480 - option D; (2) 10 days - option A; (3) 11.11% profit - option B. Read the worked steps below to see how to solve each SSC GD maths question without guessing or mixing up formulas.

SSC GD tricky maths challenge

Try each question on your own before reading its solution. Write down the information given, choose a method, and check whether your result matches an option. These questions test three useful quantitative aptitude topics: successive percentage change, combined work rates, and profit when a shopkeeper uses a false weight.

Question 1: Successive percentage change

A number is first increased by 20%, then decreased by 20%, and finally increased by 25%. The final result is 576. Find the original number.

A. 450   B. 500   C. 520   D. 480

Question 2: Time and work

A and B together can complete a work in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A, B and C together complete the work?

A. 10 days   B. 15 days   C. 12 days   D. 8 days

Question 3: Profit with a false weight

A shopkeeper uses a weight of 900 grams instead of 1 kilogram and sells goods at the cost price per kilogram. What is his profit percentage?

A. 9%   B. 11.11%   C. 10%   D. 12.5%

Step-by-step solution to Question 1

Answer: 480 (option D). Work backwards from the final value. When a number is increased by 25%, it becomes 125% of its earlier value. Therefore, just before the last increase, the number was 576 ÷ 1.25 = 460.8.

That 460.8 is after a 20% decrease, so it represents 80% of the value before the decrease. Divide by 0.8: 460.8 ÷ 0.8 = 576. The number before the decrease was 576.

The 576 was itself after the first 20% increase, so it is 120% of the original number. Original number = 576 ÷ 1.2 = 480.

Check the answer by moving forward

  1. Start with 480.
  2. Increase by 20%: 480 × 1.20 = 576.
  3. Decrease by 20%: 576 × 0.80 = 460.8.
  4. Increase by 25%: 460.8 × 1.25 = 576.

The final value matches the question, so 480 is correct. The percentage changes do not simply cancel: each percentage is calculated on the value at that stage.

Why the other options are not correct

The complete sequence multiplies the original number by 1.20 × 0.80 × 1.25 = 1.20. So the original must be 576 ÷ 1.20 = 480. Substituting 450, 500, or 520 would produce final values of 540, 600, and 624 respectively, not 576.

Step-by-step solution to Question 2

Answer: 10 days (option A). In time-and-work questions, use work rates instead of adding completion times. Let the daily rates of A, B, and C be a, b, and c, where one complete job is one unit of work.

  • A and B together: a + b = 1/12 of the work per day.
  • B and C together: b + c = 1/15 of the work per day.
  • C and A together: c + a = 1/20 of the work per day.

Add the three equations. Each worker's rate appears twice, so 2(a + b + c) = 1/12 + 1/15 + 1/20.

Use 60 as the common denominator: 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. Therefore, 2(a + b + c) = 1/5, and the combined rate of A, B, and C is 1/10 of the job per day.

If the team completes 1/10 of the work each day, the whole job takes 1 ÷ (1/10) = 10 days.

Why adding the pair times is a trap

Do not calculate 12 + 15 + 20, and do not assume the three workers' times can be added directly. The numbers 12, 15, and 20 describe how long each pair takes; convert them to rates first. The answer is 10 days, option A.

Step-by-step solution to Question 3

Answer: 11.11% profit (option B). Let the cost price of 1 kilogram be ₹100 for easy calculation. The shopkeeper charges ₹100, the cost price of a full kilogram, but gives only 900 grams.

The 900 grams actually given cost the shopkeeper ₹90 because 900 grams is 0.9 kilogram. His selling price is ₹100, so his profit is ₹100 − ₹90 = ₹10.

Profit percentage is calculated on the actual cost price of the goods supplied, not on the selling price: (₹10 ÷ ₹90) × 100 = 11.11% approximately. So option B is correct.

Use the direct false-weight formula

When a seller charges for 1 kilogram but supplies only w grams, while charging the cost price per kilogram, the profit percentage is ((1000 − w) ÷ w) × 100. Here it is ((1000 − 900) ÷ 900) × 100 = (100 ÷ 900) × 100 = 11.11%.

Why 10% is not the profit percentage

The missing 100 grams are 10% of the claimed kilogram, which can make 10% look tempting. But profit percentage uses the actual cost of 900 grams as its base. The profit is ₹10 on a cost of ₹90, not ₹10 on ₹100. That is why the answer is 11.11%, not 10%.

Fast revision guide for these SSC GD maths questions

Successive percentages: Convert each change into a multiplier. Increase by r% means multiply by 1 + r/100; decrease by r% means multiply by 1 - r/100. To reverse a sequence, undo the final change first and divide by its multiplier.

Time and work: Convert completion times into one-day work rates. Add rates for people working together. When pairwise rates are given, add all three pair equations; each person's rate is counted twice.

False weights: Compare the money received with the actual cost of the quantity delivered. Profit percentage = profit ÷ actual cost × 100. Do not use the selling price as the denominator.

Exam tips and common mistakes to avoid

  • For a chain of percentage changes, do not add or subtract the percentages. Apply each change to the new value.
  • When a question gives pair completion times, write the rate equations before doing arithmetic. Keep the unit as one complete job.
  • In profit and loss, identify the cost price of the quantity actually delivered. A false weight changes the real cost.
  • Use a quick check: substitute the selected option into the original conditions. It is an effective way to catch a calculation error.
  • Keep fractions exact until the end. Round only when the question asks for an approximate percentage.

Frequently asked questions

1. What is the correct answer to the SSC GD successive percentage question?

The original number is 480, option D. The three changes have a net multiplier of 1.20 × 0.80 × 1.25 = 1.20, so the original is 576 ÷ 1.20 = 480.

2. How do you find the time taken by A, B, and C together?

Add the three pair rates: (A+B) + (B+C) + (C+A) = 1/12 + 1/15 + 1/20 = 1/5. This counts the combined rate twice, so their actual rate is 1/10 of the work per day. They finish in 10 days.

3. Why is the false-weight profit 11.11% and not 10%?

The shopkeeper's cost for the 900 grams supplied is 90% of the one-kilogram cost, while he receives the full one-kilogram price. His profit is therefore 10 units on a cost of 90 units: 10/90 × 100 = 11.11%.

4. What is the best way to solve tricky SSC GD maths questions?

Identify the topic first, write the relevant rate or multiplier, solve step by step, and verify the result against the original question and answer choices. Avoid choosing an option just because it looks familiar.