(a) The present ages of a father and his son are in the ratio 10 : 3. If the son is 15 years old now, in how many years will the ratio of their ages be 2 : 1?
(b) The arithmetic mean of x, y and z is 6 while that of x, y, z, l, u, v and w is 9. Calculate the arithmetic mean of l, u, v and w.
Explanation
(a) Present ages of a father and his son are in the ratio 10 : 3.
Let the sum of their ages be x.
The son’s age = 15 years = (frac{3}{13} times x = 15)
(x = frac{15 times 13}{3} = 65)
(therefore) The Father’s present age = 65 – 15 = 50 years.
In z years time, the ratio of their ages = 2 : 1
(frac{50 + z}{15 + z} = frac{2}{1})
(implies 50 + z = 2(15 + z))
(50 + z = 30 + 2z implies 50 – 30 = 2z – z)
(20 = z)
Therefore, in 20 years’ time, the ratio of their age will be 2 : 1.
(b) (frac{x + y + z}{3} = 6 implies x + y + z = 18 …. (1))
(frac{x + y + z + l + u + v + w}{7} = 9 implies x + y + z + l + u + v + w = 63 …. (2))
Putting (1) into (2), we have
(18 + l + u + v + w = 63 )
(therefore l + u + v + w = 63 – 18 = 45)
Mean of l, u, v and w = (frac{45}{4} = 11.25).