Ratio, Proportion
- The ratio of the age of a father to that of his son is 5: 2. If the product of their ages in years is 1000, then the father's age (in years) after 10 years will be :
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Let father’s age be 5x years.
Son’s age = 2x years
∴ 5x × 2x = 1000
⇒ x2 = 100 ⇒ x = 10
∴ Father’s age after 10 years
= 5x + 10
= 5 × 10 + 10 = 60 yearsCorrect Option: B
Let father’s age be 5x years.
Son’s age = 2x years
∴ 5x × 2x = 1000
⇒ x2 = 100 ⇒ x = 10
∴ Father’s age after 10 years
= 5x + 10
= 5 × 10 + 10 = 60 years
- The ratio of the age of Ram and Rahim 10 years ago was 1 : 3. The ratio of their age five years hence will be 2 : 3. Then the ratio of their present age is
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Let the age of Ram and Rahim 10 years ago be x and 3x years respectively.
After 5 years from now,x + 15 = 2 3x + 15 3
⇒ 6x + 30 = 3x + 45
⇒ 3x = 45 – 30 = 15
∴ Ratio of their present age
= (x + 10) : (3x + 10)
= 15 : 25 = 3 : 5Correct Option: B
Let the age of Ram and Rahim 10 years ago be x and 3x years respectively.
After 5 years from now,x + 15 = 2 3x + 15 3
⇒ 6x + 30 = 3x + 45
⇒ 3x = 45 – 30 = 15
∴ Ratio of their present age
= (x + 10) : (3x + 10)
= 15 : 25 = 3 : 5
- At present, the ratio of the age of Maya and Chhaya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Maya’s present age is
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Let Maya’s present age be 6x years and Chhaya’s present age be 5x years.
After 15 years,6x + 15 = 9 5x + 15 8
⇒ 48x + 120 = 45x + 135
⇒ 48x – 45x = 135 – 120
⇒ 3x = 15 ⇒ x = 5
∴ Maya’s present age = 6x
= 6 × 5 = 30 yearsCorrect Option: C
Let Maya’s present age be 6x years and Chhaya’s present age be 5x years.
After 15 years,6x + 15 = 9 5x + 15 8
⇒ 48x + 120 = 45x + 135
⇒ 48x – 45x = 135 – 120
⇒ 3x = 15 ⇒ x = 5
∴ Maya’s present age = 6x
= 6 × 5 = 30 years
- The sum of the age of a father and his son is 100 years now. 5 years ago their age were in the ratio of 2 : 1. The ratio of the age of father and son after 10 years will be
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5 years ago, let the age of father = 2x years (let)
Then, Age of son = x years
∴ 2x + 5 + x + 5 = 100
⇒ 3x = 100 –10 = 90⇒ x = 90 = 30 3
∴ Father’s present age
= 2x + 5 = 60 + 5 = 65 years
Son’s present age = x + 5
= 30 + 5
= 35 years.
After 10 years,Ratio = 65 + 10 = 75 = 5 35 + 10 45 3
= 5 : 3Correct Option: A
5 years ago, let the age of father = 2x years (let)
Then, Age of son = x years
∴ 2x + 5 + x + 5 = 100
⇒ 3x = 100 –10 = 90⇒ x = 90 = 30 3
∴ Father’s present age
= 2x + 5 = 60 + 5 = 65 years
Son’s present age = x + 5
= 30 + 5
= 35 years.
After 10 years,Ratio = 65 + 10 = 75 = 5 35 + 10 45 3
= 5 : 3
- The ratio of present age of two brothers is 1 : 2 and 5 years back. the ratio was 1 : 3. What will be the ratio of their age after 5 years ?
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Let the present age of brothers be x and 2x years.
Then, 5 years ago,x − 5 : 1 2x − 5 3
⇒ 3x – 15 = 2x – 5
⇒ x = 15 – 5 = 10
∴ Age of elder brother
= 10 × 2 = 20
∴ Required ratio= 10 + 5 = 15 = 3 : 5 20 + 5 25 Correct Option: C
Let the present age of brothers be x and 2x years.
Then, 5 years ago,x − 5 : 1 2x − 5 3
⇒ 3x – 15 = 2x – 5
⇒ x = 15 – 5 = 10
∴ Age of elder brother
= 10 × 2 = 20
∴ Required ratio= 10 + 5 = 15 = 3 : 5 20 + 5 25
