SSC CHSL Tier 2 mathematics

In Tier 1, a wrong maths answer costs half a mark against two for a right one. In Tier 2, a wrong answer costs a full mark against three. The topics hardly change, but that one rule, together with the fact that Tier 2 builds your merit, should change how you attempt the paper. Tier 2 maths rewards careful, confident attempts, not a race to finish.

What changes from Tier 1

Because maths and reasoning share one clock in Section I, you choose the split. Many candidates finish reasoning in 25–30 minutes and give maths the rest, which works out to roughly a minute per maths question. Our Tier 2 strategy guide covers the whole-paper plan.

The arithmetic of attempts

• A blind guess among four options has an expected value of 1/4 × 3 − 3/4 × 1 = 0. It adds risk and nothing else.
• After eliminating two options, the expected value is 1/2 × 3 − 1/2 × 1 = +1. That guess is worth taking.
• After eliminating one, it is 1/3 × 3 − 2/3 × 1 = +1/3. That's a small gain, so take it only if you are confident about the elimination.

Now compare two candidates. One attempts 26 questions and gets 24 right: 72 − 2 = 70. The other attempts all 30 and still gets 24 right: 72 − 6 = 66. The four extra attempts cost four marks. Aim for 90% accuracy or better on what you attempt.

How to break a multi-step question

Tier 2 questions often chain two topics: markup then discount then a fee, or two pipes where one is closed midway. Four habits make them routine:

1. Assume a convenient base, such as CP = 100 or total work = LCM of the times.
2. Do one step per line on the rough sheet. Don't combine steps in your head.
3. Name the quantity asked before you start: profit %, the remaining time, the total or the difference.
4. Sanity-check the result against the options and common sense. A profit after a heavy discount can't exceed the markup.

Six worked Tier 2-style questions

Q1. A shopkeeper marks an item 40% above cost, gives a 15% discount, and pays 2% of the selling price as a card-processing fee. Find the net profit percentage.
Take CP = 100. MP = 140. SP = 140 × 0.85 = 119. The fee is 2% of 119 = 2.38, leaving 116.62. Profit = 16.62%.

Q2. ₹10,000 is invested at 10% a year, compounded half-yearly, for one year. Find the interest.
Half-yearly means 5% for two periods: 10,000 × 1.05 × 1.05 = 11,025. Interest = ₹1,025.

Q3. If x + 1/x = 6, find x⁴ + 1/x⁴.
x² + 1/x² = 6² − 2 = 34. Square again: x⁴ + 1/x⁴ = 34² − 2 = 1,156 − 2 = 1,154.

Q4. Pipes A and B can fill a tank in 12 and 15 hours. Both are opened, and A is closed after 4 hours. How much longer does B take to fill the tank?
Total = 60 units. A = 5 and B = 4 an hour. In 4 hours they fill 36, leaving 24 for B at 4 an hour: 6 hours.

Q5. Two trains, 120 m and 180 m long, run in opposite directions at 54 km/h and 36 km/h. How long do they take to cross each other?
Relative speed = 90 km/h = 25 m/s. Distance = 120 + 180 = 300 m. Time = 300 ÷ 25 = 12 seconds.

Q6. A solid cylinder of radius 7 cm and height 12 cm is melted and recast into a cone of the same radius. Find the cone's height.
Volume is conserved: πr² × 12 = ⅓πr² × h, so h = 3 × 12 = 36 cm. π and r² cancel, so there is nothing to calculate beyond the factor 3.

Topics to strengthen between tiers

• Combined arithmetic: markup with discount and profit; compound interest with half-yearly or quarterly compounding; mixtures that feed into profit.
• Algebra: identities, the x + 1/x family, and a + b + c = 0 results.
• Geometry: triangle centres, similarity and circle theorems. See our geometry guide.
• Mensuration: 3D solids, recasting and unit conversion.
• Trigonometry: identities and heights and distances.
• Data interpretation: longer tables with several questions on the same totals.

A three-week plan between tiers

Keep an error log with three columns: the question, why you got it wrong (concept, calculation or misreading), and the fix. Re-solve every logged question at the end of each week.

Common mistakes

Practice

1. An item is marked 25% above cost and sold at a 10% discount. Find the profit percentage.
2. If x − 1/x = 3, find x² + 1/x².
3. A candidate attempts 27 Tier 2 maths questions and gets 25 right. Find the score.
4. Find the difference between compound interest (compounded annually) and simple interest on ₹8,000 at 10% a year for 2 years.
5. A car covers the first half of a distance at 40 km/h and the second half at 60 km/h. Find its average speed.
6. A can do a job in 15 days and B in 20 days. They work together for 6 days, then B leaves. How long does A take to finish?
7. In triangle ABC, ∠A = 64° and I is the incentre. Find ∠BIC.
8. A solid sphere of radius 3 cm is melted into a cylinder of radius 3 cm. Find the cylinder's height.

Answers:

1. 12.5%. 125 × 0.9 = 112.5.
2. 11. 3² + 2.
3. 73. 25 × 3 − 2 × 1.
4. ₹80. P(R/100)² = 8,000 × 1/100.
5. 48 km/h. 2 × 40 × 60/(40 + 60).
6. 4.5 days. Total 60: A = 4, B = 3. In 6 days they do 42, leaving 18 for A at 4 a day.
7. 122°. 90 + 32.
8. 4 cm. (4/3)π × 27 = 36π = π × 9 × h.

What to do next

• Take one 30-question timed set and calculate your accuracy, not just your score.
• Start an error log today and re-solve it every Sunday.
• Practise 10 multi-step questions a day, writing one step per line.
• Use the maths revision sheet in the last week before Tier 2.