Answer the following MCQs on ratio and proportion:
The ratio of the present ages of Mahesh and Ajay is respectively 3 : 2. After 8 years, ratio of their ages will be 11 : 8. What will be the present age of Mahesh’s son if his age is half of the present age of Ajay ?
(a) 12 years
(b) 24 years
(c) 18 years
(d) 9 years
(e) None of these
Answer: (a)
Let present ages of Mahesh and Ajay is 3x and 2x respectively.
According to question, \(\displaystyle \frac{{3x+8}}{{2x+8}}=\frac{{11}}{8}\)
Present age of Mahesh’s son = \(\displaystyle \frac{{24}}{2}=12 years\)
Two friends P and Q started a business investing in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s. At the end of the year, 20% profit was earned which was equal to ₹ 98,000. What was the amount invested by R?
(a) ₹ 1,05,000
(b) ₹ 1,75,000
(c) ₹ 2,10,000
(d) Data inadequate
(e) None of these
Answer: (c)
Let the total investment be ₹ x.
Then, 20% of x = 98000
X = \(\displaystyle (\frac{{98000\times 100}}{{20}})=490000\)
Let the capitals of P, Q and R be ₹ 5x, ₹ 6x and ₹ 6x respectively. Then,
(5x × 12) + (6x × 12) + (6x × 6) = 490000 × 12
\(\displaystyle \Rightarrow \) 168x=490000×12
\(\displaystyle \Rightarrow \) x = \(\displaystyle (\frac{{490000\times 12}}{{168}})=35000\)
The respective ratio between the present age of Manisha and Deepali is 5 : X. Manisha is 9 years younger than Parineeta. Parineeta’s age after 9 years will be 33 years. The difference between Deepali’s and Manisha’s age is same as the present age of Parineeta. What will come in place of X?
(a) 23
(b) 39
(c) 15
(d) Cannot be determined
(e) None of these
Answer: (e)
Present age of Parineeta = 33 – 9 = 24 years
Present age of Manisha = 24 – 9 = 15 years
Present age of Deepali = 24 + 15 = 39 years
5 : x = 15 : 39
Therefore, x = \(\displaystyle \frac{{5\times 39}}{{15}}=13\)
The ratio of the salaries of A and B is 8 : 9. If A’s salary is increased by 50% and B’s salary is reduced by 25%, their ratio becomes 16 : 9. What is the salary of A ?
