Phrases Previous Year Questions (PYQs) – Percentages – Page 1 of 2

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

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✅ 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 $$\boxed{{\displaystyle 3400}}$$

Percentage Word Problem

Given:

• 60% students passed the half-yearly exam.
• Of them, 70% passed the annual exam.
• From the remaining 40% (who failed half-yearly), 80% passed the annual exam.

Assume total students = 100

✅ From 60 students who passed half-yearly:
→ 70% of 60 = 42 passed annual exam.

✅ From 40 students who failed half-yearly:
→ 80% of 40 = 32 passed annual exam.

✅ Total students who passed annual exam = 42 + 32 = 74
Final Answer: 74%

Let the total number of students = N

We know,

• 78% students were successful → 22% students failed.
• Number of failures = 176.

So,

22% of N = 176
⇒ 22N / 100 = 176
⇒ N = (176 × 100) / 22 = 800

Total students appeared = 800

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Now, 34% got first class:

First class students = 34% of 800
= (34 × 800) / 100
= 272

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✅ Final Answer: 272 students got first class.

Let the original fraction be N/D.

According to the problem:

• Numerator is increased by 25% → New numerator = 1.25N
• Denominator is decreased by 20% → New denominator = 0.8D

So, new fraction =
(1.25N) / (0.8D) = 5/4

Simplify:
(1.25 / 0.8) × (N/D) = 5/4
(1.25 ÷ 0.8) = 1.5625 = 25/16

⇒ (25/16) × (N/D) = 5/4

⇒ N/D = (5/4) × (16/25)
= 80 / 100
= 4/5

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✅ Final Answer: The original fraction = 4/5

 Ritu's Profit Percentage on Bananas

Step 1: Ritu purchased 20 dozen bananas.
Cost per dozen = ₹375

Total cost price (CP) = 20 × 375 = ₹7500

Total number of bananas = 20 × 12 = 240

Selling price (SP) per banana = ₹33

Total SP = 240 × 33 = ₹7920

Step 2: Calculate Profit

Profit = SP − CP = 7920 − 7500 = ₹420

Profit % = (Profit / CP) × 100 = (420 / 7500) × 100 = 5.6%

✅ Final Answer: 5.6%

Hemant's Monthly Salary Calculation

Step 1: Let Hemant's monthly salary be x.

He deposits 10% in PF ⇒ PF = 0.10x

Remaining salary after PF = 0.90x

Step 2: Savings

He saves 30% of the remaining ⇒ Savings = 0.30 × 0.90x = 0.27x

Remaining after savings = 0.90x - 0.27x = 0.63x

Step 3: Expenses on Medicine and Groceries

The ratio is given: Medicine : Groceries = 3 : 4

Total ratio parts = 3 + 4 = 7

Medicine = (3/7) × 0.63x = 0.27x

Step 4: Given that medicine expense = Rs. 2700

0.27x = 2700

⇒ x = 2700 ÷ 0.27 = ₹10,000

✅ Final Answer: ₹10,000

Percentage Puzzle: Exam Pass Analysis

Step-by-Step Breakdown:

• Assume total students = 100
• Passed in Half-Yearly = 60 students
• 70% of 60 passed in Annual = 42 students
• Failed in Half-Yearly = 40 students
• 80% of 40 passed in Annual = 32 students
• Total passed in Annual = 42 + 32 = 74 students

✅ Final Answer: 74% of the students passed the annual exam.