Question

My mother is 12 years more than twice my age. After 8 years, my mother’s age will be 20 years less than three times my age. Find my age and my mother’s age.

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Answer 1

Answer:

lets my age is x year and my mothers age y years currently

so

2x+12 = y ---------------------eq1

after 8 years

3(x+8) -20 = y+8 -------------------eq2

from eq 1 and 2

3(x+8) -20 = 2x+12+8

=> 3x + 24 - 20 = 2x + 12 + 8

=> 3x-2x = 12 + 8 + 20 - 24

=> x = 16

from eq 1

2x+12 = y

=> y = 2 *16 + 12

=> y = 44

so

my current age is 16 years an my mother's current age is 44 years

Answer 2

Answer:

Child's age is 16 years

Mother's age is 44 years

Explanation:

Solution :

Consider,

• Child's age = a
• Mother's age = 2a + 12

After 8 years,

Child's age = a + 8

Mother's age = 2a + 12 + 8

★ According to the Question :

$\longrightarrow$ 3 (a + 8) - 20 = 2a + 12 + 8

$\longrightarrow$ 3a + 24 - 20 = 2a + 20

$\longrightarrow$ 3a + 4 = 2a + 20

$\longrightarrow$ 3a - 2a = 20 - 4

$\longrightarrow$ a = 16

Child's age = 16 years

Mother's age = 2a + 12

$\longrightarrow$ 2 (16) + 12

$\longrightarrow$ 32 + 12

$\longrightarrow$ 44

Mother's age = 44 years

Therefore,

Child's age is 16 years

Mother's age is 44 years