Cost of 8 pencils 5 pens and 3 erasers is Rs 111 Cost of 9 pencils 6 pens and 5 erasers is Rs 130 Co...........

Quantitative Aptitude and Numerical Ability (DRDO) (Phase-i and II) Algebra

Cost of 8 pencils, 5 pens and 3 erasers is Rs. 111. Cost of 9 pencils, 6 pens and 5 erasers is Rs. 130. Cost of 16 pencils, 11 pens and 3 erasers is Rs. 221. What is the cost (in Rs) of 39 pencils, 26 pens and 13 erasers?

546

356

538

258

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Explanation:

Let the price of single pencil, pen, and eraser be x, y, and z respectively
According to question,
8x + 5y + 3z = Rs. 111 ----(1)
9x + 6y + 5z = Rs. 130 ----(2)
16x + 11y + 3z = Rs. 221 ----(3)
Subtracting equation (1) from (3)
⇒ (16x + 11y + 3z) - (9x + 6y + 5z) = 221 - 111
⇒ 8x + 6y = 110
⇒ 4x + 3y = 55 ----(4)
Multiply the equation (2) by 3 and (3) by 5 and then subtracting equation (2) from (3)
⇒ (16x + 11y + 3z) × 5 - (9x + 6y + 5z) × 3 = 221 × 5 - 130 × 3
⇒ 80x + 55y + 15z - 27x - 18y - 15z = 1105 - 390
⇒ 53x + 37y = 715 ----(5)
Multiply the equation (4) by 53 and (5) by 4 and then subtracting equation (4) from (5)
⇒ 212x + 159y - 212x - 148y = 2915 - 2860
⇒ 11y = 55
⇒ y = 5By putting the value of y = 5 in equation (4)
⇒ 4x + 3 × 5 = 55
⇒ x = 10
By putting the value of y = 5 and x = 10 in equation (1)
⇒ 8 × 10 + 5 × 5 + 3z = 111
⇒ 80 + 25 + 3z = 111
⇒ z = 2
∴ Cost of 39 pencils, 26 pens and 13 erasers is 39x + 26y + 13z =39 × 10 + 26 × 5 + 13 × 2 = Rs. 546