1. The age of sonal and manoj are in the ratio 7:5. Ten years hence, the ratio of their ages will be 9:7. Find their present ages.

2. Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

3. Raju is 19 years younger than his cousin. After 5 years, their ages will be in the ratio 2:3. Find their present ages.

4.After 12 years manoj will be 3 times as old as he was 4 years ago. Find his present age.

5. In a examination, a student requires 40% of the total marks to pass. If Rupa gets 185 marks and fails by 15 marks, find the total marks

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1)

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https://www.meritnation.com/ask-answer/question/question-the-ages-of-leena-and-heena-are-in-the-ratio-7-5/simple-equations/2856026

2)

Let the present ages of father and son be F and S respectively.
According to the question,
5 years ago,
F – 5 = 7 (S – 5) … (1)
5 years hence,
F + 5 = 3 (S + 5) … (2)
Subtracting equation (1) from equation (2),
(F + 5) – (F – 5) = 3 (S + 5) – 7 (S – 5)
F + 5 – F + 5 = 3S + 15 – 7S + 35
10 = –4S + 50
4S = 50 – 10
4S = 40
S = 40 ÷ 4 = 10
By putting this value into equation (1),
F – 5 = 7 (10 – 5)
F – 5 = 7 × 5
F – 5 = 35
F = 35 + 5
F = 40
Present age of son = 10 years
Present age of father = 40 years

 

4)

Let the preset age of Raj be x years.

Age of Manoj after 12 years = (x + 12) years

Age of manoj 4 years ago = (x – 4) years

Given, Age of manoj after 12 years = 3 × Age of Manoj 4 years ago

∴ (x + 12 ) = 3 (x – 4)

⇒ x + 12 = 3x – 12

⇒ 2x = 24

 x = 12

 

Thus, present age of manoj is 12 years.

 

5)

Let the total marks be x.
Pass mark = 40% of x
Rupa gets 185 marks and fails by 15 marks.
∴ Pass mark = 185 + 15
⇒ 40% of x = 200
Thus, the total mark in the exam is 500.

 

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