Phrases Previous Year Questions (PYQs) – Quantitative Aptitude – Page 1 of 3

Solution:
Ratio = $2:5\Rightarrow \frac{2S}{7},\frac{5S}{7}$
CI on $\frac{2S}{7}$ for 2 yrs @ $20\mathrm{\%}=$ $0.44\times \frac{2S}{7}=\frac{0.88S}{7}$
SI on $\frac{5S}{7}$ for 2 yrs @ $R\mathrm{\%}=$ ${\displaystyle \frac{5S}{7}}\times {\displaystyle \frac{R\times 2}{100}}={\displaystyle \frac{RS}{70}}$
Equating ⇒ $\frac{0.88S}{7}={\displaystyle \frac{RS}{70}}$
$\therefore R=8.8\mathrm{\%}\text{p.a.}$

Let the original number = x

Step 1: Condition

Increased by 15% ⇒ New value = 1.15x

Given: 1.15x = 161

Step 2: Solve

x = 161 ÷ 1.15

x = 140

---

✅ Final Answer: The original number is 140.

Assume total population = 100.

Given, ratio of adults to children = 2:3.

Thus,
Adults = $\frac{2}{5}\times 100=40$
Children = $\frac{3}{5}\times 100=60$

Among adults:
Literate adults = $59.9\mathrm{\%}$ of 40 = $$\frac{59.9}{100}\times 40=23.96$$
Among children:
Literate children = $85.1\mathrm{\%}$ of 60 = $$\frac{85.1}{100}\times 60=51.06$$
Total literate people = $$23.96+51.06=75.02$$
Thus, percentage of literates = $$\frac{75.02}{100}\times 100=75.02\mathrm{\%}\approx \boxed{{\displaystyle 75\mathrm{\%}}}$$

Let the total number of candidates who appeared from Maharashtra = $x$.

From Maharashtra, 9% of candidates got selected. Hence, the number of selected candidates from Maharashtra = $$0.09x$$
Let the total number of candidates who appeared from Tripura = $y$.

From Tripura, 12% of candidates got selected. Hence, the number of selected candidates from Tripura = $$0.12y$$
According to the problem, the number of selected candidates from Tripura is 102 more than those selected from Maharashtra. Hence, $$0.12y=0.09x+102$$
Also, we are given that the number of candidates who appeared from both states is equal: $$x=y$$
Substitute $y=x$ into the equation: $$0.12x=0.09x+102$$ Simplify: $$0.12x-0.09x=102$$ $$0.03x=102$$ $$x=\frac{102}{0.03}=3400$$
Thus, the number of candidates who appeared from both Maharashtra and Tripura is $$\boxed{{\displaystyle 3400}}$$