Question

Two numbers are in the ratio 2: 5. If 16 is added to both the numbers, their ratio becomes 1: 2. The numbers are: (1) 16, 40 (2) 20, 50 (3) 28, 70 (4) 32, 80

Answer 1

Step-by-step explanation:

let the numbers be x and y

x and y are in the ratio 2:5

x/y = 2/5

5x = 2y

5x-2y = 0 —(1)

Now, 16 is added to both the numbers

x+16/y+16 = 1/2

2x + 32 = y + 16

2x-y = -16 —(2)

multiply (2) by 2,

4x - 2y = -32 —(3)

Solving (1) and (3) by elimination method,

5x - 2y = 0

4x - 2y = -32

- + +

x = 32

y = 80

option (4) is correct

Answer 2

Answer:

Let the ratio 2: 5 be 2x & 5x

A/Q,

2x + 16 + 5x + 16 = 1x + 2x [taking 1: 2 as

1x & 2x]

7x + 32 = 3x

32 = 3x - 7x

32 = - 4x

32/4 = x

8 = x

Therefore, x = 8

Now,

2x= 2 x 8 | 5x = 5 x 8

= 16 | = 40

So option (1) is correct