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Let us assume the the ages of A and B be 3x and 11x years.
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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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.
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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Let us assume the present age of Radha be Y years; then
Before 6 years Radha's age will be Y - 6 years.
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 1^{1}/_{4} times her age at the time of marriage,
5/4 ( Y - 6 ) = Y ( Since 1^{1}/_{4} = 5/4 )
⇒ 5Y - 30 = 4Y
∴ Y = 30 years
Hence, her son's age = 30 x 1/10 =3 years
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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.
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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Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively.
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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