🌟 Ratio & Proportion – Easy Notes
1. Ratio – Kya hota hai?
Socho aapke paas 10 toffees hain aur aapke dost ke paas 5 toffees.
Aap dono ke toffee ka comparison karna hai → 10:5 = 2:1.
👉 Matlab ratio ek comparison tool hai – do cheezon ko compare karta hai “kitni
zyada/kitni kam”.
2. Proportion – Kya hota hai?
Agar do ratios equal ho jaayein to usse proportion bolte hain.
Example:
2:3 = 4:6 ✔ (Dono ka value same hai → proportion).
👉 Simple words me: Ratio = comparison, Proportion = equality of two comparisons.
3. Daily Life Examples
● School: Class me ladke : ladki = 3:2.
● Shopping: 2 kg apples ka price 100 hai, to 4 kg ka price automatically 200 hoga →
proportion.
● Work: 4 workers ko ek kaam khatam karne me 10 din lagte hain, to 8 workers ko
aadha time lagega (inverse proportion).
👉 Matlab ratio-proportion life ke har corner me use hota hai.
, 4. Important Short Formulas
● Ratio of a to b = a:ba:ba:b
● Proportion: a:b=c:d⇒ad=bca:b = c:d \Rightarrow ad = bca:b=c:d⇒ad=bc
● Divide Q in ratio a:b →
First part = aa+b×Q\frac{a}{a+b} \times Qa+ba×Q,
Second part = ba+b×Q\frac{b}{a+b} \times Qa+bb×Q.
● Direct proportion: x1x2=y1y2\frac{x_1}{x_2} = \frac{y_1}{y_2}x2x1=y2y1
● Inverse proportion: x1y1=x2y2x_1y_1 = x_2y_2x1y1=x2y2
5. Exam-Oriented Examples
Q1. ₹500 ko 3:2 ratio me baantna hai.
→ First share = (3/5)×500 = ₹300, Second = ₹200.
Q2. 4 men work = 12 days. 6 men work = ?
→ (4×12)/6 = 8 days.
Q3. A:B = 2:3, B:C = 4:5 → A:B:C = ?
→ A:B = 2:3 = 8:12, B:C = 4:5 = 12:15 → A:B:C = 8:12:15.
6. Why Important for Exams?
Ratio & Proportion ki wajah se exam me aapko Age problems, Partnership, Mixture &
Alligation, Work & Time ke questions easily solve karne milte hain.
Agar formulas + thoda practice yaad hai, to yeh topic fastest scoring ban jaata hai.
✅ In short:
Ratio aur Proportion ek “maths ki language” hai jo hume cheezon ko compare aur
distribute karna sikhati hai. Daily life se lekar exams tak – dono me yeh ekdum must
hai.
1. Ratio – Kya hota hai?
Socho aapke paas 10 toffees hain aur aapke dost ke paas 5 toffees.
Aap dono ke toffee ka comparison karna hai → 10:5 = 2:1.
👉 Matlab ratio ek comparison tool hai – do cheezon ko compare karta hai “kitni
zyada/kitni kam”.
2. Proportion – Kya hota hai?
Agar do ratios equal ho jaayein to usse proportion bolte hain.
Example:
2:3 = 4:6 ✔ (Dono ka value same hai → proportion).
👉 Simple words me: Ratio = comparison, Proportion = equality of two comparisons.
3. Daily Life Examples
● School: Class me ladke : ladki = 3:2.
● Shopping: 2 kg apples ka price 100 hai, to 4 kg ka price automatically 200 hoga →
proportion.
● Work: 4 workers ko ek kaam khatam karne me 10 din lagte hain, to 8 workers ko
aadha time lagega (inverse proportion).
👉 Matlab ratio-proportion life ke har corner me use hota hai.
, 4. Important Short Formulas
● Ratio of a to b = a:ba:ba:b
● Proportion: a:b=c:d⇒ad=bca:b = c:d \Rightarrow ad = bca:b=c:d⇒ad=bc
● Divide Q in ratio a:b →
First part = aa+b×Q\frac{a}{a+b} \times Qa+ba×Q,
Second part = ba+b×Q\frac{b}{a+b} \times Qa+bb×Q.
● Direct proportion: x1x2=y1y2\frac{x_1}{x_2} = \frac{y_1}{y_2}x2x1=y2y1
● Inverse proportion: x1y1=x2y2x_1y_1 = x_2y_2x1y1=x2y2
5. Exam-Oriented Examples
Q1. ₹500 ko 3:2 ratio me baantna hai.
→ First share = (3/5)×500 = ₹300, Second = ₹200.
Q2. 4 men work = 12 days. 6 men work = ?
→ (4×12)/6 = 8 days.
Q3. A:B = 2:3, B:C = 4:5 → A:B:C = ?
→ A:B = 2:3 = 8:12, B:C = 4:5 = 12:15 → A:B:C = 8:12:15.
6. Why Important for Exams?
Ratio & Proportion ki wajah se exam me aapko Age problems, Partnership, Mixture &
Alligation, Work & Time ke questions easily solve karne milte hain.
Agar formulas + thoda practice yaad hai, to yeh topic fastest scoring ban jaata hai.
✅ In short:
Ratio aur Proportion ek “maths ki language” hai jo hume cheezon ko compare aur
distribute karna sikhati hai. Daily life se lekar exams tak – dono me yeh ekdum must
hai.
