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Problem Based on ages

  1. The ratio of ages of A and B is 3 : 11. After 3 years the ratio becomes 1:3. What are the ages of A and B?
    1. 9 years, 33 years
    2. 10 years, 40 years
    3. 9 years, 27 years
    4. None of these
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    Let us assume the the ages of A and B be 3x and 11x years.

    Correct Option: A

    Let us assume the ages of A and B be 3x and 11x years; then
    After 3 years the ages of A and B will be 3x + 3 and 11x + 3.
    According to question,
    After 3 years the ratio of the ages becomes 1: 3,
    (3x + 3)/(11x + 3) = 1/3
    ⇒ 3 (3x + 3) = 1 (11x + 3)
    ⇒ 9x + 9 = 11x + 3
    ⇒ 2x = 6
    ∴ x = 3
    Hence, their present age, 3x = 3 x 3 = 9 years; 11x = 11 x 3 =33 years

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  1. In 10 years A will be twice as old as B was 10 years ago. If A is now 9 years older than B, what is the present age of B?
    1. 38 years
    2. 39 years
    3. 40 years
    4. 41 years
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    Method 1
    Let us assume the present age of B and A be x and ( x + 9 ) years.

    Method 2
    Let us assume the present age of B and A be x and y years.

    Correct Option: B

    Method 1
    Let the present age of B and A be x and ( x + 9 ) years; then,
    Age of B and A after 10 years will be x + 10 and x + 9 + 10;
    According to question,
    In 10 years A will be twice as old as B was 10 years ago
    2(x - 10) = x + 9 + 10
    2x - 20 = x + 19
    ⇒ 2x - x = 19 + 20
    ∴ x = 39 years

    Method 2
    Let us assume the present age of B and A be x and y years.
    According to question,
    A is now 9 years older than B,
    y = x + 9...........(1)
    Again according to question,
    In 10 years A will be twice as old as B was 10 years ago
    y + 10 = 2( x - 10)................. (2)
    now put the value of y from equation (1) in above equation (2)
    x + 9 +10 = 2x - 20
    ⇒ 2x - x = 19 + 20
    ⇒ x = 39 years
    So Present age of B = 39 years.

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  1. Radha get married 6 years ago. Today her age is 11/4 times her age at the time of marriage. Her son's age is 1/10 times her age. Her son's age is :
    1. 1 years
    2. 2 years
    3. 3 years
    4. 4 years
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    Let us assume the present age of Radha be Y years; then
    Before 6 years Radha's age will be Y - 6 years.

    Correct Option: C

    Let us assume the present age of Radha be Y years; then
    Before 6 years Radha's age will be Y - 6 years.
    According to question,
    Today her age is 11/4 times her age at the time of marriage,
    5/4 ( Y - 6 ) = Y ( Since 11/4 = 5/4 )
    ⇒ 5Y - 30 = 4Y
    ∴ Y = 30 years
    Hence, her son's age = 30 x 1/10 =3 years

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  1. Two years ago, the ratio of Ram's and Mohan's age was 3 : 2 and at present 7 : 5. What are their present ages?
    1. 14 years, 10 years
    2. 15 years, 10 years
    3. 13 years, 9 years
    4. None of these
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    The ratio of Ram's and Mohan's present age is 7 : 5.
    Let us assume the present ages of Ram and Mohan are 7Y and 5Y years.

    Correct Option: A

    The ratio of Ram's and Mohan's present age is 7 : 5.
    Let us assume the present ages of Ram and Mohan are 7Y and 5Y years.
    2 Years ago the age of Ram and Mohan will be 7Y - 2 and 5Y - 2 years.
    According to question,
    Two years ago, the ratio of Ram's and Mohan's age was 3 : 2, then
    (7Y -2)/(5Y - 2) = 3/2
    ⇒ (7Y -2) x 2 = 3 x (5Y - 2)
    ⇒ 14Y - 4 = 15Y - 6
    ∴ Y = 2
    Hence, their present ages = 7 x 2 = 14 years and 5 x 2 = 10 year

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  1. One year ago, the ratio of Yamini and Gamini's was 6 : 7 respectively. Four year hence, the ratio would become 7 : 8. Find the age of Gamini ?
    1. 30 years
    2. 32 years
    3. 36 years
    4. 40 years
    5. .
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    Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively.

    Correct Option: C

    Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively; then
    (6P + 5)/(7P + 5) = 7/8
    ⇒ (6P + 5) x 8 = 7 x (7P + 5)
    ⇒ 48P + 40 = 49P + 35
    ∴ P = 5
    Hence, present ago of Gamini = 7P + 1 = 7 x 5 + 1 = 36 years

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