NCERT Solutions for Class 7th Maths Chapter 7 .4 A Pinch of History — In-text Questions

Book page 183 – 1847 Updated on2026-09-19

Q1.

Example 16: Bījgaṇita by Bhāskarāchārya (1150 CE) mentions this problem. One man has ₹300 rupees and 6 horses. Another man has 10 horses and a debt of ₹100. If they are equally rich and the price of each horse is the same, tell me the price of one horse.

Answer

One horse costs ₹100.

Let the price of one horse be ₹x.

First man's wealth = 300 + 6x
Second man's wealth = 10x − 100 (a debt of ₹100 is − 100)

They are equally rich, so
300 + 6x = 10x − 100
300 + 6x + 100 = 10x (add 100 to both sides)
400 + 6x = 10x
400 = 10x − 6x (subtract 6x from both sides)
400 = 4x
x = 400 ÷ 4 = ₹100

Check: first man has 300 + 6 × 100 = ₹900. Second man has 10 × 100 − 100 = ₹900. Equally rich ✓

Why it happens: a debt counts as negative wealth, which is why the second man's total is 10x − 100 and not 10x + 100. The second man has 4 more horses but is ₹400 poorer in cash (₹300 owned against ₹100 owed). For the two to come out level, those 4 horses must be worth exactly ₹400.

Did you know? Bhāskarāchārya set this problem in verse in the twelfth century. The unknown was written yā (short for yāvat-tāvat, "as much as needed"), and known numbers were marked rū (for rūpa). Our x is his yā.

Q2.

Let us look at a few equations of the following form: 5x + 4 = 3x + 8, or 3x – 6 = 2x + 4. Can we come up with a formula to solve these equations? That is, for the first equation, can we perform some operations using 5, 4, 3, and 8 that will directly give us the solution? Using a similar method, can you solve the second equation using the numbers 3, – 6, 2 and 4?

Answer

Yes. Both equations have the form Ax + B = Cx + D, and Brahmagupta's rule gives the solution straight from the four numbers.

Ax + B = Cx + D
Ax − Cx = D − B (subtract Cx and subtract B from both sides)
(A − C)x = D − B
x = (D − B) ÷ (A − C)

Equation	A, B, C, D	x = (D − B) ÷ (A − C)	Solution
5x + 4 = 3x + 8	5, 4, 3, 8	(8 − 4) ÷ (5 − 3) = 4 ÷ 2	x = 2
3x − 6 = 2x + 4	3, − 6, 2, 4	(4 − (− 6)) ÷ (3 − 2) = 10 ÷ 1	x = 10

Checks: 5(2) + 4 = 14 and 3(2) + 8 = 14 ✓ 3(10) − 6 = 24 and 2(10) + 4 = 24 ✓

Why it happens: the formula is not magic — it is the ordinary method done once, in general. Bring the unknowns to the left and the plain numbers to the right; the unknown terms leave (A − C)x and the numbers leave D − B. Doing this with letters means nobody has to repeat the steps ever again.

Tip: be careful with signs. In the second equation B is − 6, so D − B = 4 − (− 6) = 10.

Q3.

Using this formula can you solve this equation 2x + 3 = 4x + 5?

Answer

x = − 1.

Here A = 2, B = 3, C = 4, D = 5.
x = (D − B) ÷ (A − C)
x = (5 − 3) ÷ (2 − 4)
x = 2 ÷ (− 2) = − 1

Check: LHS = 2(− 1) + 3 = 1. RHS = 4(− 1) + 5 = 1. ✓

Why it happens: A − C is negative this time (2 − 4 = − 2), and a positive divided by a negative is negative — so the answer is negative. The formula copes with negative numbers by itself; you only have to keep the signs straight.

Check it yourself the long way: 2x + 3 = 4x + 5 → 3 − 5 = 4x − 2x → − 2 = 2x → x = − 1. The formula and the full method agree.

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