Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Option killerविकल्प-छँटनीRarely taughtकम सिखाई जाने वाली✓ Checked on 6,560 cases✓ 6,560 मामलों पर जाँची गई
Option killer: the digit-sum check
Use it when:कब इस्तेमाल करें: Exact multiplication, addition or subtraction questions where all the options are close.
Reduce each number to its digit sum, repeating until one digit (4,327 → 16 → 7).
Do the same operation on these single digits and reduce again.
The correct option must have the same digit sum. Usually only one does.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: A number and its digit sum leave the same remainder when divided by 9, and remainders survive addition, subtraction and multiplication (“casting out nines”).
Limits:सीमाएँ: Cannot tell apart options that differ by a multiple of 9, and does not work for division or decimals. Pair it with the last-digit check.
Exam strategyपरीक्षा रणनीतिRarely taughtकम सिखाई जाने वाली✓ Checked on 49 cases✓ 49 मामलों पर जाँची गई
Round in opposite directions, and only as much as the options allow
Use it when:कब इस्तेमाल करें: Approximation questions and DI with long numbers.
Look at the gap between the two closest options as a % of the answer.
Your total rounding error (roughly the sum of each number’s % rounding) must stay well below that gap.
Round one number up and the next one down so the errors cancel.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: For products and quotients, relative errors add: (1 + e₁)(1 + e₂) ≈ 1 + e₁ + e₂. Opposite roundings have opposite signs and cancel.
Limits:सीमाएँ: When options are within 2–3% of each other, calculate exactly (and use the digit-sum check).
Mental mathsमानसिक गणित✓ Checked on 8,640 cases✓ 8,640 मामलों पर जाँची गई
Compare two ratios without dividing
Use it when:कब इस्तेमाल करें: DI questions like “in which year was the ratio highest?” or “which is greater, 37/53 or 41/59?”.
a/b > c/d exactly when a × d > b × c (for positive numbers).
For growth rates, compare (new/old) the same way: no percentages needed.
Exampleउदाहरण
37/53 or 41/59?
→ 37 × 59 = 2,183 and 53 × 41 = 2,173, so 37/53 is bigger.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: Multiplying both sides of a/b > c/d by the positive number b·d keeps the inequality and removes the division.
Limits:सीमाएँ: Positive numbers only; with negative values the direction can flip.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Data interpretation (table) · Easyआसान
Wheat production (in lakh tonnes). 2020: Punjab 270, Haryana 90; 2021: Punjab 90, Haryana 180; 2022: Punjab 170, Haryana 190; 2023: Punjab 180, Haryana 130; 2024: Punjab 260, Haryana 220. In 2024, the figure for Haryana is what percent of that for Punjab? (rounded to 2 decimals)
Wheat production (in lakh tonnes)
Year
Punjab
Haryana
2020
270
90
2021
90
180
2022
170
190
2023
180
130
2024
260
220
84.62%
118.18%
76.62%
94.62%
Answer:उत्तर:84.62%
220 ÷ 260 × 100 = 84.62%.
Example 2उदाहरण 2 · Bar chart: percentage change between two years · Easyआसान
The bar chart shows Ashoka Steel’s production (in thousand tonnes). What is the percentage decrease in production in 2024 compared with 2023?
6%
24.49%
32.43%
75.51%
Answer:उत्तर:24.49%
2023: 245; 2024: 185.
Change = -60.
Decrease % = 60 ÷ 245 × 100 = 24.49%.
Example 3उदाहरण 3 · Pie chart: amounts, ratios and central angles · Easyआसान
The pie chart shows how the Patel family spends its monthly income of ₹1,10,000. How much is spent on Others?
₹3,000
₹9,166.67
₹33,000
₹33,500
Answer:उत्तर:₹33,000
Others = 30% of ₹1,10,000.
= 30 × 1,10,000 ÷ 100 = ₹33,000.
Example 4उदाहरण 4 · Line graph: averages and the steepest rise · Easyआसान
The line graph shows the monthly sales of a patna sweet shop. What were the average monthly sales from January to June?
142.5
147.5
148.33
178
Answer:उत्तर:148.33
Total = 145 + 125 + 160 + 170 + 150 + 140 = 890.
Average = 890 ÷ 6 = 148.33.
Example 5उदाहरण 5 · Table: ratios and shares of a total · Easyआसान
In 2020, what percentage of Ganga Retail’s total units sold were Mobiles?
Ganga Retail: units sold (units)
Year
Tablets
Mobiles
Laptops
2019
160
125
135
2020
140
190
70
2021
105
165
100
2022
170
125
70
2023
160
180
175
24.2%
33.33%
47.5%
90.48%
Answer:उत्तर:47.5%
Total in 2020 = 140 + 190 + 70 = 400.
Share = 190 ÷ 400 × 100 = 47.5%.
Example 6उदाहरण 6 · Data interpretation (table) · Mediumमध्यम
Two-wheeler sales (in thousands). 2020: Hero 90, Bajaj 160; 2021: Hero 110, Bajaj 90; 2022: Hero 100, Bajaj 90; 2023: Hero 100, Bajaj 180; 2024: Hero 110, Bajaj 100. What is the percentage change for Hero from 2022 to 2024? (rounded to 2 decimals)
Two-wheeler sales (in thousands)
Year
Hero
Bajaj
2020
90
160
2021
110
90
2022
100
90
2023
100
180
2024
110
100
10% increase
9.09% increase
20% increase
10% decrease
Answer:उत्तर:10% increase
Change = 110 − 100 = 10.
10 ÷ 100 × 100 = 10% → 10% increase.
Example 7उदाहरण 7 · Bar chart: percentage change between two years · Mediumमध्यम
The bar chart shows Ashoka Steel’s production (in thousand tonnes). What is the percentage decrease in production in 2022 compared with 2019?
3.5%
14%
16.28%
86%
Answer:उत्तर:14%
2019: 250; 2022: 215.
Change = -35.
Decrease % = 35 ÷ 250 × 100 = 14%.
Example 8उदाहरण 8 · Pie chart: amounts, ratios and central angles · Mediumमध्यम
In the pie chart of the Sharma family’s spending, what is the central angle of the Savings sector?
90°
15°
108°
54°
Answer:उत्तर:54°
Angle = 15% × 360° ÷ 100.
= 15 × 3.6 = 54°.
Common mistakesआम गलतियाँ
Using the wrong year as the base for growth.
Reading the wrong row or unit (thousands vs lakhs).
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
How many DI questions come in IBPS PO prelims?
Usually one or two sets of about five questions each, so often 10 or more questions in total.
How do I get faster at DI?
Build calculation speed (the Aptitude Gym helps), read questions first, and approximate.
What chart types appear?
Tables, bar graphs, line graphs, pie charts and caselets. More chart types are coming to this practice set.