Question

The ratio between the present ages of A and B is 3:5 respectively. If the
difference between B's present age and A's age after 4 years is 2 , what
is the total of A's and B's present ages?
A. 24 years
C. 48 years
B. 32 year
D. cannot be determined​

Answer 1

Step-by-step explanation:

$a = 3x$

$b = 5x$

$5x - (3x + 4) = 2$

$5x - 3x - 4 = 2$

$2x = 6$

$x = 3$

$a = 9yrs$

$b = 15yrs$

$(a + b) = (9 + 15) = 24yrs(a.)$

Answer 2

The total of A's and B's present ages = 24 years [ The correct option is A. 24 years ]

Given :

• The ratio between the present ages of A and B is 3 : 5 respectively.

• The difference between B's present age and A's age after 4 years is 2

To find :

The total of A's and B's present ages

A. 24 years

B. 32 years

C. 48 years

D. cannot be determined

Solution :

Step 1 of 2 :

Form the equation to calculate total of A's and B's present ages

Here it is given that ratio between the present ages of A and B is 3 : 5 respectively

Let present ages of A and B is 3x years and 5x years respectively

A's age after 4 years is (3x + 4) years

Since difference between B's present age and A's age after 4 years is 2

So by the given condition

$\displaystyle \sf 5x - (3x + 4) = 2$

Step 2 of 2 :

Calculate total of A's and B's present ages

$\displaystyle \sf 5x - (3x + 4) = 2$

$\displaystyle \sf{ \implies }5x - 3x - 4 = 2$

$\displaystyle \sf{ \implies }2x - 4 = 2$

$\displaystyle \sf{ \implies }2x = 6$

$\displaystyle \sf{ \implies }x = 3$

Present age of A

= 3x years

= 3 × 3 years

= 9 years

Present age of A

= 5x years

= 5 × 3 years

= 15 years

∴ Total of A's and B's present ages

= 9 years + 15 years

= 24 years

Hence the correct option is A. 24 years

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