RRB NTPC Mathematics Practice Questions

RRB NTPC Mathematics Practice Questions – May 26, 2025

1. Time & Work

Question: P and Q can complete a job in 12 and 16 days respectively. They work together for 4 days. What portion of the work is left?

Solution:

• LCM of 12 and 16 = 48 units (Total work)

• P’s 1-day work = 48/12 = 4 units

• Q’s 1-day work = 48/16 = 3 units

• Combined 1-day work = 4 + 3 = 7 units

• Work done in 4 days = 7 × 4 = 28 units

• Remaining work = 48 – 28 = 20 units

• Fraction left = 20/48 = 5/12

                    Answer: 5/12   by RRB NTPC Mathematics Practice  Questions

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2. Mensuration

        Question: A cone of height 32 cm and base radius 8 cm is melted and recast into a sphere. Find the radius of the sphere.

        Solution:

• Volume of cone = (1/3)πr²h = (1/3)π×8²×32 = (1/3)π×64×32

• Volume of sphere = (4/3)πR³

• Equating volumes: (1/3)π×64×32 = (4/3)πR³

• Simplify: 64×32 = 4R³ ⇒ R³ = (64×32)/4 = 512

• R = ∛512 = 8 cm

        Answer: 8 cm

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3. Profit & Loss

      Question: An article sold for Rs. 3360 yields a 12% profit. What should be the selling price for an 8% profit?

           Solution:

• Cost Price (CP) = 3360 / (1 + 12/100) = 3360 / 1.12 = Rs. 3000

• New Selling Price (SP) = 3000 × (1 + 8/100) = 3000 × 1.08 = Rs. 3240

             Answer: Rs. 3240

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4. LCM & HCF

       Question: Find the HCF of the numbers: 2×3²×5², 5×3×2², and 5²×3×2².

        Solution:

• Prime factors:

  • First: 2×3²×5²

  • Second: 2²×3×5

  • Third: 2²×3×5²

• Common factors: 2×3×5 = 30

       Answer: 30

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5. Efficiency Ratio

      Question: P and Q can complete a task in 15 and 20 days respectively. What is the ratio of their efficiencies?

          Solution:

• Efficiency  ∝ 1/Time

• Ratio = 1/15 : 1/20 = 20:15 = 4:3

           Answer: 4:3

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6. Profit Percentage Comparison

            Question: Which transaction offers the highest profit percentage?

• Option A: CP = Rs. 40, Profit = Rs. 15

• Option B: CP = Rs. 60, Profit = Rs. 24

• Option C: CP = Rs. 36, Profit = Rs. 18

• Option D: CP = Rs. 50, Profit = Rs. 24

    Solution:

• Option A: (15/40)×100 = 37.5%

• Option B: (24/60)×100 = 40%

• Option C: (18/36)×100 = 50%

• Option D: (24/50)×100 = 48%

         Answer: Option C (50%)

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7. Trigonometry

       Question: Evaluate: tan10° × tan15° × tan80° × tan75°

          Solution:

• tan80° = cot10°, tan75° = cot15°

• Expression becomes: tan10°×tan15°×cot10°×cot15° = (tan10°×cot10°)×(tan15°×cot15°) = 1×1 = 1

         Answer: 1