Question

2:3. Find the numbers. 11. Two numbers are in the ratio of 3:5. If 8 is added to each number, the ratio becomes 2:3. Find the numbers.​

Answer 1

Two numbers are in the ratio of 2:3

So, yx=32

Cross multiply to get: 3x=2y

Or, 3x−2y=0   …..(1)

If 8 is added in both numbers the ratio becomes 3:4

So, (y+8)(x+8)=43

Cross multiply to get: 4(x+8)=3(y+8)

Or, 4x+32=3y+24

Or, 4x−3y=−8   …….(2)

Multiplying Eq1 by 4 and Eq 2 by 3 we have:

12x−8y=0      ………(3)

12x−9y=−24 …………(4)

Solving Eq3 and Eq4 we have y=24 and x=16

Answer 2

Answer:

$Let the required numbers be 3x and 5x Given that if 8 is added to each other then ratio becomes 2: 3 That is 3x + 8: 5x + 8 = 2: 3 (3x + 8)/ (5x + 8) = 2/3 3 (3x + 8) = 2 (5x + 8) 9x + 24 = 10x + 16 By transposing 24 – 16 = 10x – 9x x = 8 Thus the numbers are 3x = 3 (8) = 24 And 5x = 5 (8) = 40w./two-numbers-are-in-the-ratio-5-if-is-added-to-each-number-the-ratio-becomes-2-find-the-numbers$

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