Question

Ratio of two numbers is 15:19. If 2 is added to each number their ratio becomes 4:5
Find the sum of the numbers
a. 34
b. 68
C. 78
d. 38​

Answer 1

Answer:

Two numbers = 15x, 19x

15x+2 = 4y        19x+2 = 5y

Subtract, 19x+2-15x-2=5y-4y

              4x = y

Substitute y = 4x , 15x+2 = 16x

                            x = 2

         15x = 30       19x = 38

Sum of the two numbers = 30+38 = 68

Answer 2

Answer:

★ (b) 68 ★

Step-by-step explanation:

Given:

• Ratio of two numbers is 15:19.
• If 2 is added to each number, their ratio becomes 4:5.

To find:

• The sum of the numbers.

Solution:

Let the 1st number be 15x and the 2nd number be 19x.

• If 2 is added to the first number, the number will be = (15x+2)

• If 2 is added to the 2nd number, the number will be = (19x+2)

According to the question,

• If 2 is added to each number, their ratio becomes 4:5.

$\implies$ (15x+2):(19x+2)=4:5

$\implies$ (15x+2)/(19x+2)=4/5

$\implies$ 76x+8=75x+10

$\implies$ 76x-75x=10-8

$\implies$ x=2

Therefore,

• 1st number = (15×2)=30
• 2nd number = (19×2)=38

Sum of the numbers ,

= (30+38)

= 68

${\boxed{\sf{Option\:(b)\:68\:is\:the\: correct\: answer.}}}$

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