Dosto, ab aaya Maths ka sabse scoring chapter! Percentage ka matlab hai "per 100" — yaani har 100 mein kitna. 25% = 25/100 = 1/4. Bas itni si baat!
CET Group D mein isse seedhe 1–2 questions aate hain, PAR asli baat ye hai: Profit-Loss, Discount, Simple & Compound Interest, Data Interpretation — ye saare chapters percentage par hi chalte hain. Yani ek chapter, faayda 5 chapters mein!
Isliye ye chapter thoda lamba hai aur detail mein hai. Fraction-percentage table zaroor ratt lena — wahi speed ka asli raaz hai. Chalo shuru! 💪
1. Percentage ka Matlab
- x% = x/100. Jaise 25% = 25/100 = 1/4, aur 150% = 1.5 (100% se zyada bhi ho sakta hai!).
- x% of y = (x/100) × y. Jaise 15% of 300 = (15/100) × 300 = 45.
- A kitne % hai B ka = (A/B) × 100. Jaise 15, 60 ka = (15/60)×100 = 25%.
- Fraction ko % banao: × 100. 1/8 → (1/8)×100 = 12.5%. % ko fraction banao: ÷ 100.
2. Fraction ↔ Percentage Table (ISE RATT LO! ⭐)
Ye table yaad hai to aadha calculation mind mein hi ho jayega — exam mein sabse bada hathiyar:
| Fraction | % | Fraction | % |
|---|---|---|---|
| 1/1 | 100% | 1/9 | 11.11% (11⅑) |
| 1/2 | 50% | 1/10 | 10% |
| 1/3 | 33.33% (33⅓) | 1/11 | 9.09% |
| 1/4 | 25% | 1/12 | 8.33% (8⅓) |
| 1/5 | 20% | 1/16 | 6.25% |
| 1/6 | 16.67% (16⅔) | 1/20 | 5% |
| 1/7 | 14.28% | 1/25 | 4% |
| 1/8 | 12.5% | 1/40 | 2.5% |
Aise hi: 33⅓% = 1/3 · 16⅔% = 1/6 · 12.5% = 1/8 · 6.25% = 1/16.
3. Percentage Increase / Decrease
| Kya nikalna hai | Formula |
|---|---|
| % Increase | (Badhotri ÷ PURANI value) × 100 |
| % Decrease | (Kami ÷ PURANI value) × 100 |
| x% increase ke baad nayi value | Purani × (100+x)/100 |
| x% decrease ke baad nayi value | Purani × (100−x)/100 |
Step 1: Badhotri = 500 − 400 = 100
Step 2: % = (100 ÷ 400) × 100 = 25% ✓ (nichey hamesha PURANI value, 500 nahi!)
4. Successive (do baar) Percentage Change — ⭐ FORMULA
Step 2: Net = 20 − 20 + (20 × −20)/100 = 0 − 4 = −4%
Matlab: 4% ki KAMI (barabar nahi hua!). Check: 100 → 120 → 96 ✓
5. Reverse Relation (A, B se x% zyada… wale sawal)
| Diya hai | Poocha hai | Formula |
|---|---|---|
| A, B se x% zyada | B, A se kitna % kam? | x/(100+x) × 100 |
| A, B se x% kam | B, A se kitna % zyada? | x/(100−x) × 100 |
Step 1: 25/(100+25) × 100 = 25/125 × 100 = 20% ✓
Shortcut soch: B = 100, A = 125. Difference 25, par ab neeche A (125) lagega → 25/125 = 20%.
6. Price aur Consumption (kharcha same rakhna)
Matlab: Kharcha utna hi rakhna hai to cheeni ka istemal 20% kam karo ✓
Step 1: Dono ka passing mark barabar likho: 30% + 45 = 45% − 15
Step 2: 15% = 60 → Total = 60 × 100/15 = 400 ✓
Step 3: Passing marks = 30% of 400 + 45 = 120 + 45 = 165
Step 1: Dusre ko 40% mile → antar = 60 − 40 = 20%
Step 2: 20% = 1200 → Total = 1200 × 100/20 = 6000 ✓
Step 1: 10000 × 110/100 = 11000 (pehla saal)
Step 2: 11000 × 110/100 = 12,100 ✓ (formula: P(1 + r/100)ⁿ — ye CI jaisa hi hai!)
Step 1: 25x = 20y (dono taraf 100 cancel)
Step 2: x/y = 20/25 = 4/5 → x : y = 4 : 5 ✓
Step 1: 20/(100−20) × 100 = 20/80 × 100 = 25% ✓
(100 → 80; 80 se 100 par jaana = 20/80 = 25% badhotri. "Kam wala % chhota, badhane wala % bada" — hamesha!)
Step 1: Formula: a + b − (ab)/100 = 10 + 20 − 200/100 = 28%
Check: 100 → 90 → 72, yani 28 ki chhoot ✓ (30% NAHI hota — ye sabse common trap hai!)
16% of 25 = 25% of 16 = 4
Jo aasan lage wo taraf se karo. 8% of 50 = 50% of 8 = 4. Ye trick exam mein 20 second bachati hai!
37.5% = 3/8 · 16⅔% = 1/6 · 12.5% = 1/8
37.5% of 800 → (3/8) × 800 = 300. % ko fraction banao, phir seedha multiply — division ka jhanjhat khatam.
10% = point ek jagah peeche
35% of 240 → 10% = 24, to 30% = 72, aur 5% = 12 → total 84. Har % ko 10% + 5% ke tukdon mein todo.
Kami = x²/100 %
20% badha phir 20% ghata → 400/100 = 4% kami. 10% par 1%, 30% par 9%. Formula lagane ki zaroorat hi nahi!
x% zyada → x/(100+x) · x% kam → x/(100−x)
25% zyada → 25/125 = 20% kam. 20% kam → 20/80 = 25% zyada. Bas dhyan rakho neeche kis par tulna ho rahi hai.
| Situation | Formula / Value |
|---|---|
| x% of y | (x/100) × y = y% of x |
| A, B ka kitna % | (A/B) × 100 |
| % increase/decrease | Change ÷ purani value × 100 |
| Successive a%, b% | a + b + ab/100 |
| x% up phir x% down | x²/100 % ki kami |
| x% zyada → ulta | x/(100+x) × 100 |
| x% kam → ulta | x/(100−x) × 100 |
| Daam ↑x%, kharch same | Consumption x/(100+x) × 100 % kam |
| n saal baad population | P(1 + r/100)ⁿ |
| 50% · 25% · 20% | 1/2 · 1/4 · 1/5 |
| 33⅓% · 16⅔% · 12.5% | 1/3 · 1/6 · 1/8 |
| 14.28% · 11.11% · 9.09% | 1/7 · 1/9 · 1/11 |
Q1. What is 15% of 300?
Q2. 15 is what percent of 60?
Q3. If a number is first increased by 20% and then decreased by 20%, the net change is:
Q4. A's salary is 25% more than B's salary. B's salary is less than A's by:
Q5. If 40% of a number is 120, then the number is:
Q6. A student scores 30% and fails by 45 marks, while another scores 45% and gets 15 marks more than the passing marks. The maximum marks are:
Q7. The price of sugar is increased by 25%. By what percent must a family reduce its consumption so that the expenditure remains the same?
Q8. Two successive discounts of 10% and 20% are equivalent to a single discount of:
Q9. The population of a town is 10,000 and it increases by 10% every year. Its population after 2 years will be:
Q10. 1/8 expressed as a percentage is:
Q11. If 25% of x = 20% of y, then x : y is:
Q12. In an election between two candidates, the winner got 60% of the votes and won by 1200 votes. The total number of votes polled is:
Q13. If 60% of a number is 42, then 25% of the same number is:
Q14. A man's salary is reduced by 20%. By what percent must it be increased to restore the original salary?
Percentage matlab "per 100" — x% of y = y% of x (ulta karke aasan banao). % change nikalte waqt neeche hamesha purani value aati hai. Do baar change ho to seedha jodo mat — a + b + ab/100 lagao (10% + 20% discount = 28%, 30% nahi). Same % badh ke ghate to hamesha x²/100 % ka nuksaan. Reverse sawalon mein "neeche kaun" dekho: 25% zyada = 20% kam, 20% kam = 25% zyada. Aur sabse zaroori — fraction ↔ % table (1/8 = 12.5%, 1/6 = 16⅔%, 1/7 = 14.28%) ratt lo, isse Profit-Loss aur SI-CI bhi aadhe ho jayenge! 🚀