NCERT Solutions Ganita Prakash Chapter 3 In-text Questions — Mental Math

Book page 65 & 66 Updated on2026-09-05

Q1.

Observe the figure below. What can you say about the numbers and the lines drawn? Draw arrows from the middle to the numbers on the sides to obtain the desired sums. (Middle column: 25,000; 400; 13,000; 1,500; 60,000. Sides: 38,800; 28,000; 61,600; 31,000; 3,400; 63,000; 19,500; 20,900.)

Answer

Each number on the side is built by adding numbers from the middle column, using any of them as many times as you like. The lines show which middle numbers were used.

Side number	How to make it from the middle column	Check
38,800	25,000 + 400 × 2 + 13,000	25,000 + 800 + 13,000 = 38,800 ✓
28,000	25,000 + 1,500 × 2	25,000 + 3,000 = 28,000 ✓
61,600	60,000 + 400 × 4	60,000 + 1,600 = 61,600 ✓
31,000	25,000 + 1,500 × 4	25,000 + 6,000 = 31,000 ✓
3,400	1,500 + 1,500 + 400	3,000 + 400 = 3,400 ✓
63,000	60,000 + 1,500 × 2	60,000 + 3,000 = 63,000 ✓
19,500	13,000 + 1,500 × 3 + 400 × 5	13,000 + 4,500 + 2,000 = 19,500 ✓
20,900	13,000 + 1,500 × 5 + 400	13,000 + 7,500 + 400 = 20,900 ✓

Tip: start from the biggest middle number that is not more than your target, then fill the gap. For 61,600 begin with 60,000; only 1,600 is left, and 1,600 = 400 × 4.

Q2.

Can we make 1,000 using the numbers in the middle? Why not? What about 14,000, 15,000 and 16,000? Yes, it is possible. Explore how. What thousands cannot be made?

Answer

1,000 cannot be made.

Why not: the only middle number smaller than 1,000 is 400, and adding 400s gives 400, 800, 1200, 1600 … — it skips right over 1000. Every other middle number (1,500, 13,000, 25,000, 60,000) is already bigger than 1,000.

14,000, 15,000 and 16,000 can all be made:

14,000 = 1,500 × 8 + 400 × 5 = 12,000 + 2,000 ✓
15,000 = 13,000 + 400 × 5 = 13,000 + 2,000 ✓
16,000 = 13,000 + 1,500 × 2 = 13,000 + 3,000 ✓

Which thousands cannot be made? Only 1,000. Every other whole thousand can be built:

Target	One way to make it	Target	One way to make it
2,000	400 × 5	7,000	1,500 × 2 + 400 × 10
3,000	1,500 × 2	8,000	400 × 20
4,000	400 × 10	9,000	1,500 × 6
5,000	1,500 × 2 + 400 × 5	10,000	1,500 × 4 + 400 × 10
6,000	1,500 × 4	11,000	1,500 × 6 + 400 × 5

Math Talk: notice that 400 × 5 = 2,000 and 1,500 × 2 = 3,000. Once you can make 2,000 and 3,000, you can make every thousand from 2,000 upwards just by combining them.

Q3.

Adding and Subtracting. Here, using the numbers in the boxes, we are allowed to use both addition and subtraction to get the required number. An example is shown: 39,800 = 40,000 – 800 + 300 + 300. Find 45,000 = , 5,900 = , 17,500 = , 21,400 = (boxes: 40,000; 7,000; 300; 1,500; 12,000; 800)

Answer

Now subtraction is allowed too, which makes the target much easier to hit.

Target	One correct way	Check
45,000	40,000 + 12,000 − 7,000	52,000 − 7,000 = 45,000 ✓
5,900	7,000 − 800 − 300	6,200 − 300 = 5,900 ✓
17,500	12,000 + 7,000 − 1,500	19,000 − 1,500 = 17,500 ✓
21,400	40,000 − 12,000 − 7,000 + 1,500 − 300 − 800	21,000 + 1,500 − 1,100 = 21,400 ✓

The last one uses every box exactly once. Step by step:

40,000 − 12,000 = 28,000
28,000 − 7,000 = 21,000
21,000 + 1,500 = 22,500
22,500 − 300 = 22,200
22,200 − 800 = 21,400 ✓

Tip: look at the last digits first. To end in 400 you need 1,500 − 300 − 800 = 400. The thousands then take care of themselves.

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