XAT 2012 Question 77

Question 77

Three truck drivers, Amar, Akbar and Anthony stop at a road side eating joint. Amar orders 10
rotis, 4 plates of tadka, and a cup of tea. Akbar orders 7 rotis, 3 plates of tadka, and a cup of tea. Amar pays 80 for the meal and Akbar pays 60. Meanwhile, Anthony orders 5 rotis, 5 plates of tadka and 5 cups of tea. How much (in ) will Anthony pay?

Solution

Let cost of 1 roti, 1 tadka and 1 tea be Rs. $$x, y, z$$ respectively.

Acc to ques,

=> $$10x + 4y + z = 80$$ <-- Equation 1

and $$7x + 3y + z = 60$$ <-- Equation 2

We have three equations and two unknowns. So let us try to find the value of $$x$$ and $$y$$ in terms of $$z$$.

Multiplying Equation 1 with 3 and subtracting 4 times (Equation 2) from it gives,

$$3*(10x+4y+z)-4*(7x+3y+z)=3*80-4*60$$

Or, $$2x-z =0$$

=> $$x = \frac{z}{2}$$

Substituting it in Equation 1, we get $$6z+4y=80$$ or $$y = 20 - \frac{3}{2} z$$

To find : $$5x + 5y + 5z = ?$$

= $$5 [\frac{z}{2} + (20 - \frac{3 z}{2}) + z]$$

= $$5 \times 20 = 100$$



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