Pair of linear equations · 3 marks

The cost of one paratha and 2 bowls of dahi is ₹90. Also, the cost of 2 parathas and 7 bowls of dahi is ₹260. Can you figure out the cost of one paratha and one bowl of dahi and explain your reasoning?

Answer: One bowl of dahi = ₹803 ≈ ₹26.67; one paratha = ₹1103 ≈ ₹36.67. (Doubling the first order gives 2 parathas + 4 dahi = ₹180; the second order has 3 more dahi and costs ₹80 more, so 3 dahi = ₹80.)

Step-by-step solution

Given: 1 paratha + 2 dahi = ₹90; 2 parathas + 7 dahi = ₹260
To find: Cost of one paratha and of one bowl of dahi

Idea: Make the number of parathas the same in both orders by doubling the first one. Then the only difference between the orders is extra dahi, and the extra cost tells us its price.

Let one paratha cost ₹p and one bowl of dahi ₹d. Then p + 2d = 90 … (1) and 2p + 7d = 260 … (2).1 mark
Double (1): 2p + 4d = 180 … (3). That is, 2 parathas and 4 dahi would cost ₹180.½ mark
Subtract (3) from (2): (2) has the same 2 parathas but 3 more bowls of dahi and costs 260 − 180 = ₹80 more. So 3d = 80, d = 803 ≈ ₹26.67.1 mark
From (1): p = 90 − 2 × 803 = 90 − 1603 = 1103 ≈ ₹36.67. These are not whole rupees, but they fit both bills exactly.½ mark

One paratha costs ₹110/3 (about ₹36.67) and one bowl of dahi costs ₹80/3 (about ₹26.67).

Check: (1): 1103 + 1603 = 2703 = 90 ✓. (2): 2203 + 5603 = 7803 = 260 ✓.

Answer to write in the exam

Let paratha = ₹p, dahi = ₹d

p + 2d = 90 … (1); 2p + 7d = 260 … (2)

(1) × 2: 2p + 4d = 180 … (3)

(2) − (3): 3d = 80 ⇒ d = 803 ≈ 26.67

p = 90 − 1603 = 1103 ≈ 36.67

∴ Paratha ≈ ₹36.67, dahi ≈ ₹26.67

Common mistakes that cost marks

Subtracting the two bills straight away (260 − 90 = 170) and calling that one item’s price. The orders differ in both items, so first make one item match.
Rounding d to ₹27 early and then getting p = ₹36; the check then fails (36 + 54 = 90 but 72 + 189 = 261).
Assuming the answer must be whole rupees and giving up when it is not.

How this can come in the exam

Case-based (4 marks)

At a canteen, 1 samosa and 3 cups of tea cost ₹55, while 2 samosas and 1 cup of tea cost ₹40.
(i) Write the two equations. (ii) Find the cost of one samosa and one cup of tea. (iii) What do 3 samosas and 2 cups of tea cost?

Show answer

(i) s + 3t = 55, 2s + t = 40 (1 mark). (ii) Double the first: 2s + 6t = 110; subtract the second: 5t = 70 ⇒ t = 14; s = 55 − 42 = 13 (2 marks). (iii) 39 + 28 = ₹67 (1 mark).

Try one yourself

2 pens and 3 notebooks cost ₹110; 4 pens and 7 notebooks cost ₹240. Find each price.