Quick answers: (1) A's share is approximately ₹4,065.57 - option C; (2) 60 km in still water takes 6 hours 40 minutes - option B; (3) the principal is ₹5,000 - option A. Each solution below shows the formula, the arithmetic, and a quick check so you can understand the method rather than memorize an answer.

SSC GD Maths - Tricky Challenge 4

Try each problem before reading its explanation. First identify what the question asks for, then write the relevant rate, ratio, or interest formula. Keep the units and the percentage base clear throughout the calculation.

Question 1: Divide money using simple interest

A sum of ₹8,000 is divided between A and B such that A's amount after 2 years at 10% simple interest is equal to B's amount after 3 years at 8% simple interest. Find A's original share.

A. ₹4,000   B. ₹4,500   C. ₹4,065.57 approximately   D. ₹4,200

Question 2: Boat and stream

A boat travels 36 km downstream in 3 hours and 24 km upstream in 4 hours. How long will it take to travel 60 km in still water?

A. 6 hours   B. 6 hours 40 minutes   C. 5 hours   D. 7 hours

Question 3: Compound interest compared with simple interest

The difference between the compound interest and simple interest on a sum for 2 years at 10% per annum is ₹50. Find the principal.

A. ₹5,000   B. ₹5,500   C. ₹4,000   D. ₹4,500

Step-by-step solution to Question 1

Answer: ₹4,065.57 approximately (option C). Let A's original share be ₹x. Since the total is ₹8,000, B's original share is ₹(8,000 - x).

With simple interest, amount = principal × (1 + rate × time). A's money earns simple interest for 2 years at 10%, so A's amount becomes x × (1 + 0.10 × 2) = 1.20x. B's share earns simple interest for 3 years at 8%, so B's amount becomes (8,000 - x) × (1 + 0.08 × 3) = 1.24(8,000 - x).

The question says the final amounts are equal:

1.20x = 1.24(8,000 - x)

Expand the right side: 1.20x = 9,920 - 1.24x. Add 1.24x to both sides: 2.44x = 9,920. Therefore x = 9,920 ÷ 2.44 = ₹4,065.5737..., or about ₹4,065.57.

5-step shortcut for the ₹8,000 share question

  1. Convert each simple-interest rate into an amount multiplier. A grows by 10% × 2 = 20%, so A's multiplier is 1.20. B grows by 8% × 3 = 24%, so B's multiplier is 1.24.
  2. Use the equal-maturity condition. Since both final amounts are equal, 1.20A = 1.24B.
  3. Reverse the multipliers to get the original-share ratio. A:B = 1.24:1.20 = 124:120 = 31:30. The larger growth factor belongs to the smaller original share.
  4. Divide the total into ratio units. There are 31 + 30 = 61 units, so one unit is ₹8,000 ÷ 61.
  5. Take A's 31 units and match the option. A = 31 × (₹8,000 ÷ 61) = ₹248,000 ÷ 61 ≈ ₹4,065.57 (option C). B's share is about ₹3,934.43.

Check the result

A's final amount is approximately ₹4,065.57 × 1.20 = ₹4,878.69. B's final amount is approximately ₹3,934.43 × 1.24 = ₹4,878.69. The maturity amounts match, as required.

Step-by-step solution to Question 2

Answer: 6 hours 40 minutes (option B). First find the boat's speed in each direction. Downstream speed = distance ÷ time = 36 ÷ 3 = 12 km/h. Upstream speed = 24 ÷ 4 = 6 km/h.

Let the boat's speed in still water be b and the stream's speed be s. Downstream, the current helps the boat, so b + s = 12. Upstream, the current slows it, so b - s = 6. Add the equations: 2b = 18, so b = 9 km/h. (The stream speed is 3 km/h.)

In still water, the boat travels 60 km at 9 km/h. Time = distance ÷ speed = 60 ÷ 9 = 20/3 hours = 6⅔ hours. Two-thirds of an hour is 2/3 × 60 = 40 minutes. Therefore the travel time is 6 hours 40 minutes.

Why the speeds are averaged

The still-water speed is halfway between downstream and upstream speeds because one current speed is added and the same current speed is subtracted. (12 + 6) ÷ 2 = 9 km/h. Do not average the two travel times or use the downstream speed for the still-water trip.

Step-by-step solution to Question 3

Answer: ₹5,000 (option A). Let the principal be ₹P and the annual rate be 10%, or 0.10.

For 2 years, simple interest is SI = P × 0.10 × 2 = 0.20P. With annual compounding, the amount after 2 years is P × 1.1 × 1.1 = 1.21P, so compound interest is CI = 1.21P - P = 0.21P.

The difference is CI - SI = 0.21P - 0.20P = 0.01P. The question says that difference is ₹50, so 0.01P = 50. Divide by 0.01: P = ₹5,000.

Quick check with ₹5,000

At 10% simple interest for 2 years, SI = ₹5,000 × 0.10 × 2 = ₹1,000. With annual compounding, the first year's interest is ₹500 and the second year's interest is ₹550, so CI = ₹1,050. The difference is ₹1,050 - ₹1,000 = ₹50, exactly as stated.

How to solve these SSC GD maths questions

Simple interest and shares: Turn each person's interest period into an amount multiplier. Set the two final amounts equal, use the total-share condition, and solve for the original share.

Boats and streams: Downstream speed = boat speed + stream speed; upstream speed = boat speed - stream speed. Add the two speeds and divide by two to get still-water speed.

Two-year CI versus SI: For annual compounding over exactly two years, the difference is P × (rate/100)². With a 10% rate this is 1% of the principal.

Exam tips and common mistakes

  • Simple interest grows linearly: use principal × rate × time. Do not compound it unless the question explicitly says so.
  • In an equal-maturity-amount problem, compare the growth multipliers before dividing the original total.
  • Keep boat speeds in km/h and distances in km. Convert only the fractional hour into minutes at the end.
  • For compound interest, the second year's interest is earned on the increased first-year amount, which is why CI exceeds SI.
  • Check your answer in the original condition. Equal final amounts, a correct direction-based speed, or a ₹50 interest difference can confirm the result.

Frequently asked questions

1. How do you find A's original share in the ₹8,000 division?

The amount multipliers are 1.20 for A and 1.24 for B. Equal final amounts mean A:B = 1.24:1.20 = 31:30. A's share is 31/61 of ₹8,000, or approximately ₹4,065.57 (option C).

2. What is the boat's speed in still water?

The downstream speed is 12 km/h and upstream speed is 6 km/h. Still-water speed is their average: (12 + 6)/2 = 9 km/h. At that speed, 60 km takes 6 hours 40 minutes.

3. What is the two-year difference between CI and SI at 10%?

For two years at annual rate r, the difference is P(r/100)². At 10%, it is 0.01P. If the difference is ₹50, the principal is ₹50/0.01 = ₹5,000.

4. Why is compound interest higher than simple interest after two years?

Under compound interest, the second year's interest is calculated on the principal plus the first year's interest. Simple interest is calculated on the original principal each year, so the compound-interest total is higher.

5. What are the answers to SSC GD Maths Tricky Challenge 4?

Question 1: approximately ₹4,065.57 (C). Question 2: 6 hours 40 minutes (B). Question 3: ₹5,000 (A).