Solve the following Multiple Choice Questions on ratio and proportion:
Samir’s age is one–fourth of his father’s age and two–third of his sister Reema’s age. What is the ratio of the ages of Samir, Reema and their father respectively ?
(a) 3 : 2 : 8
(b) 3 : 4 : 8
(c) 2 : 3 : 8
(d) 4 : 3 : 8
(e) None of these
Solution: (c)
Samir’s age = x year (let)
So, His father’s age = 4x years
Reema’s age = \(\displaystyle \frac{3}{2}xyears\)
Therefore, Required ratio = \(\displaystyle x:\frac{{3x}}{2}:4x=2:3:8\)
The ratio of the present ages of a son and his father is 1 : 5 and that of his mother and father is 4 : 5. After 2 years the ratio of the age of the son to that of his mother becomes 3 : 10. What is the present age of the father?
(a) 30 years
(b) 28 years
(c) 37 years
(d) Data inadequate
(e) None of these
Solution: (e)
\(\displaystyle \frac{S}{F}=\frac{1}{5}\) \(\displaystyle \Rightarrow \) F = 5S
Number of students studying in colleges A and B are in the ratio of 3 : 4 respectively. If 50 more students join college A and there is no change in the number of students in college B, the respective ratio becomes 5 : 6. What is the number of students in college B ?
(a) 450
(b) 500
(c) 400
(d) 600
(e) None of these
Solution: (d)
Let total number of students in college A = 3x
and total number of students in college B = 4x
After 50 more students join college A
New Ratio = \(\displaystyle \frac{{3x+50}}{{4x}}=\frac{5}{6}\)
\(\displaystyle \Rightarrow \) 18 x + 300 = 20 x
\(\displaystyle \Rightarrow \) 2x = 300
\(\displaystyle \Rightarrow \) x = \(\displaystyle \frac{{300}}{2}=150\)
Total number of students in college
B = 4x = 4 × 150 = 600
729 ml of a mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7 : 3 ?
(a) 60 ml
(b) 71 ml
(c) 52 ml
(d) 81 ml
(e) None of these
Solution: (d)
Quantity of water = \(\displaystyle \frac{2}{9}\times 729=162ml\)
Let ‘x’ be the quantity that should be added to make the ratio 7 : 3
According the question \(\displaystyle \frac{{567}}{{162+x}}=\frac{7}{3}\)
\(\displaystyle \Rightarrow \) 1701 = 1134 + 7x
\(\displaystyle \Rightarrow \) 7x = 1701 – 1134
\(\displaystyle \Rightarrow \)x = 81 ml
Three containers A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7, respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, then find the ratio of the milk to the water if the mixtures of all the three containers are mixed together.
