# TANCET 2008 Quant Question 1 : Linear Equation

## Question

An owner of a pizza stand sold small slices of pizza for Rs. 150 each and large slices for Rs. 250 each. One night he sold 5000 slices, for a total of Rs. 10.50 lakh. How many small slices were sold?

- 3000
- 2000
- 4000
- 2500
- 3500

**Correct Answer** : 2000. Choice (2)

#### Explanatory Answer

This question is a word problem in linear equations. The problem is solved by framing two linear equations from the information given in the question and solving them.

Let 's' be the number of small slices and 'b' the number of large slices sold on that night.

Therefore, s + b = 5000 ... eqn (1)

Each small slice was sold for Rs.150.

Therefore, 's' small slices would have fetched Rs.150s.

Each large slice was sold for Rs.250.

Therefore, 'b' large slices would have fetched Rs.250b.

Total value of sale = 150s + 250b = 10,50,000 (note the left hand side is in Rupees and hence we have to convert right hand also to Rupees from Lakhs of Rupees)

Or 150s + 250b = 10,50,000 ... eqn (2)

Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3)

Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000

Or b = 3000

We know that s + b = 5000

So, s = 5000 - b = 5000 - 3000 = 2000.

2000 small slices were sold.

Level of difficulty : Easy to Moderate

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