Question

(iii) 10 % of x + 20% of y = 24
And 3x - y =20. Find x and y*​

Answer 1

Answer :

x = 40 and y = 100

Step-by-step explanation :

• 10% of x + 20% of y = 24

  $\frac{10}{100} x+\frac{20}{100} y=24 \\\\ \frac{x}{10} + \frac{y}{5} =24 \\\\ \frac{x}{10} +\frac{y \times 2}{5 \times 2}=24 \\\\ \frac{x}{10} + \frac{2y}{10}=24 \\\\ \frac{x+2y}{10} =24 \\\\ x+2y =24 \times 10 \\\\ \bf x+2y = 240 ---[1]$

• 3x - y = 20 --- [2]

Multiply equation [2] by 2,

2(3x - y) = 2(20)

 6x - 2y = 40 --- [3]

Add equation [1] and equation [3],

 x + 2y + 6x - 2y = 240 + 40

       7x = 280

         x = 280/7

         x = 40

Substitute x = 40 in equation [2],

 3x - y = 20

3(40) - y = 20

120 - y = 20

     y = 120 - 20

    y = 100

∴ x = 40 and y = 100

Verification :

• Condition - 1

10% of x = (10/100) × 40 = 4

20% of y = (20/100) × 100 = 20

10% of x + 20% of y = 24

    4 + 20 = 24

         24 = 24

• Condition - 2

 3x - y = 20

3(40) - 100 = 20

 120 - 100 = 20

        20 = 20

Hence verified!