Question

The sum of ages of A, B, and C is 93 yr. Ten years ago, the ratio of their age was 2:3:4, Find the present age of A.?​

Answer 1

Answer:

Present age of A is 24 years.

Step-by-step explanation:

Question says that,

The sum of the age of A, B, and C is 93 years.

Ten years ago the age of A, B, and C was 2 : 3 : 4.

Find the present age of A.

Suppose, ten years ago the age of :

• A = $2x$ years.
• B = $3x$ years.
• C = $4x$ years.

Therefore, their present age will be :

• A = $(2x + 10)$ years.
• B = $(3x + 10)$ years.
• C = $(4x + 10)$ years.

Given :

${\implies (2x + 10) + (3x + 10) + (4x + 10) = 93}$

Solving for $\boldsymbol x :$

$\implies 2x + 10 + 3x + 10 + 4x + 10 = 93$

$\implies 9x + 30 = 93$

$\implies 9x = 93 - 30$

$\implies 9x = 63$

$\implies x = \frac{63}{9}$

$\implies x = 7$

${\therefore{ \underline{ \sf{The \: value \: of \: \boldsymbol{x} \: is \: 7}}}}$

Hence, the present age of A is :

• $(2x + 10) = \bf 24 \: years.$

Answer 2

Topic:

Ratio and proportion

Question:

The sum of ages of A, B, and C is 93 years . Ten years ago, the ratio of their age was 2:3:4 . Find the present age of A ?

Given:

• The sum of ages of A, B, and C is 93 years.

• The ratio of their ages 10 years ago which was 2:3:4.

To Find:

• The present age of A.

Solution:

Let x be their present age,

The ratio will be 2x : 3x : 4x

Now the ratio of the present age would be their ages ten years ago plus 10. So the ratio of their present age will be

➙ 2x + 10 : 3x + 10 : 4x + 10

We also know the sum of their present age which is 93 years . So according to the information we got,

➙ 2x + 10 + 3x + 10 + 4x + 10 ➞ 93

➙ 2x + 3x + 4x + 10 + 10 + 10 ➞ 93

➙ 9x + 30 ➞ 93

➙ 9x ➞ 93 - 30

➙ 9x ➞ 63

➙ x ➞ 63/9

➙ x ➞ 7

Thus, we got the value of the constant multiplying factor .

Now,

So , the age of A ten years back is

➞ 2x

➞ 2 × 7

➞ 14

The age of B ten years back is

➞ 3x

➞ 3 × 7

➞ 21

The age of C ten years back is

➞ 4x

➞ 4 × 7

➞ 28

The final results,

The present age of A is

➠ 14 + 10

➠ 24

The present age of B is

➠ 21 + 10

➠ 31

The present age of C is

➠ 28 + 10

➠ 38

Hence, we got the present age of A which is 24 .