Ratio, Proportion
- Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3:5?
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Let x years ago the ratio of their age was 3 : 5
∴ According to the question40 − x = 3 60 − x 5
⇒ 200 – 5x = 180 – 3x
⇒ 2x = 20
∴ x = 10 yearsCorrect Option: A
Let x years ago the ratio of their age was 3 : 5
∴ According to the question40 − x = 3 60 − x 5
⇒ 200 – 5x = 180 – 3x
⇒ 2x = 20
∴ x = 10 years
- The ratio between Sumit’s and Prakash’s age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit’s age to Prakash’s age after 6 years will be
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Sumit’s present age = 2x years
Prakash’s present age = 3x years
∴ 3x– 2x = 6
x = 6
∴ Required ratio
= (2 × 6 + 6) : (3 × 6 + 6)
= 18 : 24 = 3 : 4Correct Option: D
Sumit’s present age = 2x years
Prakash’s present age = 3x years
∴ 3x– 2x = 6
x = 6
∴ Required ratio
= (2 × 6 + 6) : (3 × 6 + 6)
= 18 : 24 = 3 : 4
- 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