Approximation, Missing Numbers and Operator Interchange
Approximation, Missing Numbers and Operator Interchange
The second half of simplification is speed work: round each number to the nearest easy value and pick the closest option, rebuild a missing number from an equation, or replace and interchange signs as instructed before applying BODMAS. Fraction and percentage chains of a number also belong here.
1. Rules Box
| Task | Method |
|---|---|
| Approximation | Round each number to the nearest whole or easy value (19.97 → 20, 4.99 → 5, √1600.4 → 40), then simplify |
| Approximate % | 12.03% of 499.9 → 12% of 500 = 60 |
| Missing "?" | Simplify the known side fully, then undo the operations on "?" in reverse order |
| Sign replacement | Rewrite the whole expression with the new signs first, then apply BODMAS |
| Which two signs to interchange | Test the options one by one; stop at the one that balances |
| Chain of fractions or percentages | Multiply all the fractions first, then apply to the number |
When options are far apart, round boldly; when they are close, keep one decimal place
x% of y = y% of x: 16% of 25 = 25% of 16 = 4
✗ After replacing signs, work left to right as written | ✓ Rewrite first, then follow BODMAS: × and ÷ before + and −
✗ 35% of 240 + ? = 120, so ? = 120 − 35 | ✓ Find 35% of 240 = 84 first: ? = 36
हिंदी नोट: सन्निकटन में हर संख्या को निकट की आसान संख्या में बदलिए। "?" वाले प्रश्न में ज्ञात भाग पहले हल कीजिए। चिह्न बदलने वाले प्रश्न में पहले पूरा व्यंजक नए चिह्नों से लिखिए, फिर BODMAS लगाइए।
Exam Pointer: Verified NTPC patterns: the closest approximate value of a decimal expression (May 2022 CBT-2) and evaluating an expression after the stated operators are interchanged (June 2025 Graduate CBT-1). Missing-number and fraction-chain questions had no verified NTPC shift in our check and are tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Approximate value of an expression
[PYQ: NTPC CBT-2 10-May-2022 Shift-1]
EXAM LEVEL
Q. Find the approximate value of 19.97 × 15.02 + 39.99 ÷ 8.01.
≈ 20 × 15 + 40 ÷ 8 = 300 + 5 = 305.
Answer: About 305
EXAMATLAS LEVEL
Q. Find the approximate value of √1600.4 × 24.98 ÷ 4.99 + 12.03% of 499.9.
≈ 40 × 25 ÷ 5 + 12% of 500 = 200 + 60 = 260.
Answer: About 260
Pattern 2: Find the missing number
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. 35% of 240 + ? = 120. Find ?.
35% of 240 = 84, so ? = 36.
Answer: 36
EXAMATLAS LEVEL
Q. (? ÷ 12) × 1.5 + 4.5² = 35.25. Find ?.
4.5² = 20.25, so (? ÷ 12) × 1.5 = 15. Then ? ÷ 12 = 10 and ? = 120.
Answer: 120
Pattern 3: Signs replaced or interchanged
[PYQ: NTPC Graduate CBT-1 5-Jun-2025 Shift-1]
EXAM LEVEL
Q. If + means ×, × means −, − means ÷ and ÷ means +, find 8 + 6 × 24 − 4 ÷ 3.
Rewritten: 8 × 6 − 24 ÷ 4 + 3. BODMAS: 48 − 6 + 3 = 45.
Answer: 45
EXAMATLAS LEVEL
Q. Which two signs must be interchanged to make 24 ÷ 4 × 5 + 24 − 4 = 122 correct?
As written the left side is 6 × 5 + 24 − 4 = 50. Interchanging + and × gives 24 ÷ 4 + 5 × 24 − 4 = 6 + 120 − 4 = 122. (The other pairs give different values, for example ÷ and × gives 24 × 4 ÷ 5 + 24 − 4 = 39.2.)
Answer: + and ×
Pattern 4: Chains of fractions and percentages of a number
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Find 2/5 of 3/4 of 1/3 of 1,200.
2/5 × 3/4 × 1/3 = 1/10, so the answer is 120.
Answer: 120
EXAMATLAS LEVEL
Q. 40% of 3/8 of a number is 45. Find 60% of 5/6 of the same number.
0.4 × 3/8 = 0.15, so the number = 45/0.15 = 300. Then 0.6 × 5/6 = 0.5, and half of 300 = 150.
Answer: 150
60-Second Revision
- Round boldly, then compare with the options.
- Missing number: simplify the known part, then undo operations in reverse.
- Replaced signs: rewrite first, then BODMAS.
- Fraction chains: multiply the fractions first.
Next Step: Mathematics done. Take a full-length ExamAtlas RRB NTPC 2026 mock test and attempt simplification first; these questions should take under 30 seconds each and set up time for the rest.