Advanced Numerical Ability Practice

This chapter supplements Chapter 6 with additional practice on the arithmetic topics most frequently tested in the Delhi Police Constable Numerical Ability section.

Practice Set (10 MCQs)

1. Simplify: 84 ÷ 7 + 9 × 4 − 12.
   (a) 36 (b) 34 (c) 38 (d) 32
2. A sum of ₹20,000 amounts to ₹26,000 in 3 years at simple interest. Find the rate of interest per annum.
   (a) 10% (b) 8% (c) 12% (d) 9%
3. Find the ratio of two numbers whose sum is 90 and whose difference is 18.
   (a) 3:2 (b) 2:1 (c) 5:4 (d) 4:3
4. A shopkeeper buys an article for ₹800 and sells it for ₹960. Find the profit percentage.
   (a) 20% (b) 15% (c) 25% (d) 18%
5. Find the average of the first ten natural numbers.
   (a) 5.5 (b) 5 (c) 6 (d) 5.75
6. A train 150 m long crosses a pole in 15 seconds. Find its speed in km/h.
   (a) 36 km/h (b) 30 km/h (c) 40 km/h (d) 45 km/h
7. If the cost price of 20 articles equals the selling price of 16 articles, find the profit percentage.
   (a) 25% (b) 20% (c) 30% (d) 15%
8. Find the value of: 15% of 400 + 25% of 200.
   (a) 110 (b) 100 (c) 120 (d) 90
9. A and B together can complete a piece of work in 12 days. A alone can do it in 20 days. In how many days can B alone complete it?
   (a) 30 days (b) 25 days (c) 28 days (d) 32 days
10. Find the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually.
    (a) ₹2,100 (b) ₹2,000 (c) ₹2,200 (d) ₹1,900

Answer Key with Explanations

1.(a) 84÷7=12; 9×4=36; 12+36−12=36.

2.(a) Interest = 26,000−20,000 = ₹6,000 over 3 years; rate = (6,000×100)/(20,000×3) = 10%.

3.(a) Let the numbers be x and y with x+y=90 and x−y=18; solving gives x=54, y=36, a ratio of 54:36 = 3:2.

4.(a) Profit = 960−800 = ₹160; profit percentage = (160/800)×100 = 20%.

5.(a) The first ten natural numbers sum to 55; average = 55/10 = 5.5.

6.(a) Speed = 150 m / 15 s = 10 m/s = 10×18/5 = 36 km/h.

7.(a) If CP of 20 articles equals SP of 16 articles, SP/CP per article = 20/16 = 1.25, a profit of 25%.

8.(a) 15% of 400 = 60; 25% of 200 = 50; sum = 110.

9.(a) Combined rate = 1/12; A's rate = 1/20; B's rate = 1/12−1/20 = 5/60−3/60 = 2/60 = 1/30, so B alone takes 30 days.

10.(a) Amount = 10,000×(1.10)² = 12,100; compound interest = ₹2,100.