Question

A man's age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is his present age? a) 25 years b) 30 years c) 35 years d) 40 years​

Answer 1

★ Answer -

• The present age of the man = 30 years.
• Option b) is correct.

★ To find -

• The present age of the man.

★ Step-by-step explanation -

• To find the present age of the man, let's form an equation using the information given to us.

Let -

• The man's present age be "x" years.

10 years ago -

• The man's age was "x - 10" years.

Given that -

• The man's age is 150% of what it was 10 years ago.

So -

• The man's age is "150% of (x - 10)" years.

After 10 years -

• The man's age will be "x + 10" years.

Given that -

• The man's age is 75% of what it will be after 10 years.

So -

• The man's age is "75% of (x + 10)" years.

Therefore -

$\longmapsto \sf150\% \: of \: (x - 10) = 75\% \: of \: (x + 10)$

$\longmapsto \sf \cancel\dfrac{150}{100} \times (x - 10) = \cancel\dfrac{75}{100} \times (x + 10)$

$\longmapsto \sf \dfrac{3}{2} \times (x - 10) = \dfrac{3}{4} \times (x + 10)$

$\longmapsto \sf \dfrac{3x - 30}{2} = \dfrac{3x + 30}{4}$

$\longmapsto \sf (3x - 30) \: (4) = (3x + 30) \: (2)$

$\longmapsto \sf 12x - 120 = 6x + 60$

$\longmapsto \sf 12x - 6x = 60 + 120$

$\longmapsto \sf 6x = 180$

$\longmapsto \sf x = \cancel\dfrac{180}{6}$

$\longmapsto \underline{\boxed{\sf x = 30}} \: \bigstar$

Thus -

• The man's present age is 30 years.

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Answer 2

QUESTION :

• A man's age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is his present age? a) 25 years b) 30 years c) 35 years d) 40 years

GIVEN :

• A man's age is 150 %

• 10 years ago, but 75% of what it will be after 10 years.

TO FIND :

• what it will be after 10 years. What is his present age = ?

SOLUTION :

man age = 150 %

years = 10 y

first we will using the value of a in these

question :

= 150/100 × ( a - 10) = 75/100 × ( a +10)

• age = 3/2 × ( a - 10) = 3/4 × ( a + 10)

• age = 3a - 30 / 2 = 3a + 30 /4

• age = ( 3 a - 30) × 4 = ( 3a + 30) × 2

• age = 12a - 120 = 6a + 60

• age = 12 a - 6a = 60 + 120

• age = 6a = 180

• age = a = 180/6

age = a = 30

so, man age will be 30 years