Question

Q18. 18% of A plus 15% of B plus 19% of C is equal to 17% of the sum of A, B and C. If A – B = 500 and A – C = 3400, what is the value of A + B + C? (a) 12,400 (b) 11,600 (c) 13,500 (d) None of these

Answer 1

The answer of b 13500 is so idea is

Answer 2

Answer:

(c) 13500

Step-by-step explanation:

In the question

18% of A + 15% of B + 19% of C = 17% of A, B and C

If A - B = 500

and A - C = 3400

Then the value of A + B + C

$\frac{18}{100}$×A + $\frac{15}{100}$×B +$\frac{19}{100}$×C= $\frac{17}{100}$ [A + B + C]

$\frac{1}{100}$[18A+15B+19C] = $\frac{17}{100}$[A+B+C]

18A + 15B + 19C = 17A + 17B + 17C

A - 2B + 2C = 0

A = 2B -2C

From A - B =500, A - C = 3400

2B - 2C - B = 500

B - 2C = 500     -------(i)

2B - 2C - C = 3400

2B - 3C = 3400     -------(ii)

from eq. (i)×2 - (ii)

2B - 4C = 1000

2B - 3C = 3400

      -C = - 2400

∴ C = 2400

A = 3400 + 2400

   = 5800

- B = 500 - 5800

   B = 5300

∴ A + B + C = 5800 + 5300 + 2400

                        =13500

The value of A + B + C = 13500