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Lesson 1 of 113

1. Ye topic hai kya?

Do (ya teen) logon ki umar saalon mein. Ranking height/order nahi (Ranking). Calendar weekday nahi (Calendar).

Paper kya maangta

Ab kitni umar, n saal pehle ratio kya tha, kitne saal baad A, B ka double, family ka average, pita–beta.

Pehle lock

Unknown ab ki umar pe rakho — A, B. Pehle/baad sirf ±n. Ratio ke tukde seedha umar nahi.

n saal pehleA − n
→
abA
→
n saal baadA + n

2. Farq — hamesha same

Dono ek saal mein ek-ek saal bade. Isliye A − B kabhi nahi badalta.

Farq constant
A − B = (A + n) − (B + n) = (A − n) − (B − n)
“8 saal baad farq 8 saal badh jayega” — jhoot. Farq wahi. Jo badhe wo dono ki umar, farq nahi.

3. Ratio — pehle asal umar

Ab ratio p : q aur sum S ho to:

A = p/(p+q) × S · B = q/(p+q) × S
Ya A = pk, B = qk, phir extra shart se k.
Sirf sum S aur farq D: bada (S + D)/2, chhota (S − D)/2.
Ratio 3:2 hai iska matlab 3 aur 2 saal nahi. 3k aur 2k — k nikalna padta hai.

Example: sum 50, farq 10. Bada (50+10)/2=30, chhota (50−10)/2=20. Ranking “badi than” chain alag page.

DiyaLikho
Ab p : qA = pk, B = qk
Sum S aur farq DBada = (S+D)/2, chhota = (S−D)/2
A, B se n badaA = B + n (ye farq hai, ratio nahi)
A, B ka m gunaA = mB

4. n saal pehle / baad — ratio badalta hai

Farq same rehta hai. Ratio nahi — kyunki dono mein same number judta hai, bada/chhota anupat badal jata hai.

n saal baad ratio p : q
(A + n) / (B + n) = p / q
n saal pehle: (A − n) / (B − n) = p / q
Check: umar negative na ho. 5 saal pehle beta 3 tha to ab 8 — “5 saal pehle 0” wale option galat.

Kitne saal baad A, B ka double?

A + x = 2(B + x) → x = A − 2B (tabhi jab A abhi se 2B se bada ho; warna pehle wala time, negative)

5. Average / family

Average = sum ÷ log
Sum = average × log
Ek nikalta hai to naya sum = purana sum − uski umar

Teen log AP (barabar farq): beech wali = average. Youngest = middle − d, oldest = middle + d.

6. “Jab pita utna tha jitna beta ab hai”

Yeh ranking nahi, time-shift hai. Kitne saal pehle pita ki umar = beta ki ab wali umar? Utna hi jitna unka farq.

Farq D = pita − beta (ab)
D saal pehle pita = beta-ab
Us time beta = beta − D = 2×beta − pita
Agar is formula se beta ki umar negative aaye, sawal galat padha — ya pita 2 guna se zyada bada hai, us time beta paida hi nahi hua tha. Paper mein aisa option “cannot determine / data absurd” kabhi-kabhi.

7. Sawal — basic se pro

Q1 · Basic

Ram ab 25 saal, Shyam 17. 8 saal baad unki umar ka farq?

  1. 6
  2. 8
  3. 10
  4. 16

Solution

  1. Step 1

    Ab farq = 25 − 17 = 8.

  2. Step 2

    8 saal baad dono +8. Farq wahi 8. Formula: farq constant.

AnswerB · 8
Q2 · Basic

A aur B ki umar 3 : 2. Dono ka sum 50 saal. A ki umar?

  1. 20
  2. 25
  3. 30
  4. 32

Solution

  1. Step 1

    Hisse 3 + 2 = 5. Ek hissa = 50 / 5 = 10.

  2. Step 2

    A = 3 × 10 = 30. B = 20. Check: 30 + 20 = 50, 30 : 20 = 3 : 2.

AnswerC · 30
Q3 · Medium

Pita ab beta se 3 guna. 8 saal baad pita, beta ka double hoga. Beta ab kitna?

  1. 6
  2. 8
  3. 10
  4. 12

Solution

  1. Step 1

    Beta ab = B. Pita = 3B.

  2. Step 2

    8 saal baad: pita 3B + 8, beta B + 8. Shart: 3B + 8 = 2(B + 8).

  3. Step 3

    3B + 8 = 2B + 16 → B = 8. Pita ab 24. 8 baad: 32 aur 16 — double. Theek.

AnswerB · 8
Q4 · Medium

5 saal pehle pita, beta se 4 guna tha. Ab pita 3 guna hai. Beta ki ab umar?

  1. 10
  2. 12
  3. 15
  4. 18

Solution

  1. Step 1

    Ab pita = 3B (B = beta ab).

  2. Step 2

    5 saal pehle: 3B − 5 = 4(B − 5).

  3. Step 3

    3B − 5 = 4B − 20 → B = 15. Pita 45. 5 pehle: 40 aur 10 — 4 guna. Ab 45 : 15 = 3. Theek.

AnswerC · 15
Q5 · Basic

5 logon ki average umar 32. Ek aadmi 40 saal ka nikal jata hai. Baaki 4 ki average?

  1. 28
  2. 30
  3. 31
  4. 32

Solution

  1. Step 1

    Kul sum = 32 × 5 = 160.

  2. Step 2

    Baaki sum = 160 − 40 = 120. Average = 120 / 4 = 30.

AnswerB · 30
Q6 · Medium

A, B se 6 saal bada hai. 4 saal baad unki umar 5 : 4. A ab kitna?

  1. 20
  2. 24
  3. 26
  4. 30

Solution

  1. Step 1

    A = B + 6. 4 saal baad: (B + 10) / (B + 4) = 5 / 4.

  2. Step 2

    4(B + 10) = 5(B + 4) → 4B + 40 = 5B + 20 → B = 20. A = 26.

  3. Step 3

    4 baad: 30 aur 24 = 5 : 4. Farq ab bhi 6.

AnswerC · 26
Q7 · Medium

Pita ab 48 saal. Jab pita utna tha jitna beta ab hai, tab beta 12 saal ka tha. Beta ab kitna?

  1. 24
  2. 28
  3. 30
  4. 36

Solution

  1. Step 1

    Beta ab = S. Farq D = 48 − S. D saal pehle pita = S (beta-ab).

  2. Step 2

    Us time beta = S − D = 2S − 48 = 12 → 2S = 60 → S = 30.

  3. Step 3

    Farq 18. 18 saal pehle pita 30, beta 12. Sentence match.

AnswerC · 30
Q8 · Basic

A ab 20, B 8. Kitne saal baad A, B ka exactly double hoga?

  1. 2
  2. 4
  3. 6
  4. 8

Solution

  1. Step 1

    20 + x = 2(8 + x) → 20 + x = 16 + 2x → x = 4.

  2. Step 2

    4 saal baad 24 aur 12. Double. (Ab 20, 8 ka double 16 nahi — isliye abhi nahi, 4 baad.)

AnswerB · 4
Q9 · Basic

Teen bhaiyon ki umar AP mein. Sum 48 saal, common farq 4 saal. Sabse chhote ki umar?

  1. 10
  2. 12
  3. 14
  4. 16

Solution

  1. Step 1

    Umar: a − 4, a, a + 4. Sum 3a = 48 → a = 16.

  2. Step 2

    Teen umar: 12, 16, 20. Chhota = 12.

AnswerB · 12
Q10 · Pro

A ab 24 saal. Jab A utna tha jitna B ab hai, us time B ki umar ka double hi A ki ab wali umar hai. B ab kitna?

  1. 12
  2. 16
  3. 18
  4. 20

Solution

  1. Step 1

    B ab = S. “Jab A = S tha” = (24 − S) saal pehle.

  2. Step 2

    Us time B = S − (24 − S) = 2S − 24.

  3. Step 3

    A-ab = us time B ka double: 24 = 2(2S − 24) → 12 = 2S − 24 → 2S = 36 → S = 18.

  4. Step 4

    6 saal pehle A = 18 (B-ab). Tab B = 12. A-ab 24 = 12 ka double. Sentence lock.

AnswerC · 18

Practice

Pehle khud, phir neeche kholo.

12345 678910
P1

A aur B ka farq ab 11 saal. 7 saal pehle farq?

  1. 4
  2. 7
  3. 11
  4. 18

Solution

  1. Step 1

    Farq constant. Pehle bhi 11.

AnswerC · 11
P2

Umar 2 : 3, sum 40. Chhoti umar?

  1. 14
  2. 16
  3. 18
  4. 24

Solution

  1. Step 1

    5 hissa, ek = 8. Chhoti = 2 × 8 = 16. Badi 24.

AnswerB · 16
P3

A ab B se 4 guna. 6 saal baad A, B ka 3 guna. A ab?

  1. 36
  2. 40
  3. 48
  4. 54

Solution

  1. Step 1

    A = 4B. 4B + 6 = 3(B + 6) → 4B + 6 = 3B + 18 → B = 12. A = 48.

  2. Step 2

    6 baad: 54 aur 18 = 3 guna.

AnswerC · 48
P4

10 saal pehle A, B se 5 guna tha. Unka farq 20 saal (ab bhi, kyunki farq same). A ab?

  1. 25
  2. 30
  3. 35
  4. 40

Solution

  1. Step 1

    A = B + 20. 10 pehle: B + 10 = 5(B − 10).

  2. Step 2

    B + 10 = 5B − 50 → 60 = 4B → B = 15, A = 35. 10 pehle 25 aur 5 = 5 guna.

AnswerC · 35
P5

5 logon ki average 36. Ek aadmi 40 nikalta hai. Baaki average?

  1. 33
  2. 34
  3. 35
  4. 36

Solution

  1. Step 1

    Sum 180. Baaki 140. 140 / 4 = 35.

AnswerC · 35
P6

A, B se 8 saal bada. 5 saal baad umar 7 : 5. B ab?

  1. 12
  2. 15
  3. 18
  4. 20

Solution

  1. Step 1

    A = B + 8. (B + 13) / (B + 5) = 7 / 5.

  2. Step 2

    5(B + 13) = 7(B + 5) → 5B + 65 = 7B + 35 → B = 15. A = 23. 5 baad 28 : 20 = 7 : 5.

AnswerB · 15
P7

Pita 42, beta 24. Jab pita 24 saal ka tha, beta kitna tha?

  1. 4
  2. 6
  3. 8
  4. 12

Solution

  1. Step 1

    Farq 18. 18 saal pehle pita 24. Beta tab 24 − 18 = 6. Ya 2×24 − 42 = 6.

AnswerB · 6
P8

A = 24, B = 10. Kitne saal baad A, B ka double?

  1. 2
  2. 4
  3. 6
  4. 8

Solution

  1. Step 1

    24 + x = 2(10 + x) → 24 + x = 20 + 2x → x = 4. Baad: 28 aur 14.

AnswerB · 4
P9

Teen log AP, sum 96, common farq 8. Beech wale ki umar?

  1. 24
  2. 28
  3. 32
  4. 40

Solution

  1. Step 1

    3a = 96 → a = 32. Umar 24, 32, 40. Beech = 32 = average bhi.

AnswerC · 32
P10

Beti 8, maa 32. Kitne saal baad maa, beti se 2.5 guna hogi?

  1. 4
  2. 6
  3. 8
  4. 10

Solution

  1. Step 1

    32 + x = 2.5(8 + x) → 32 + x = 20 + 2.5x → 12 = 1.5x → x = 8.

  2. Step 2

    8 baad: 40 aur 16. 40 / 16 = 2.5.

AnswerC · 8

← Index · Calendar

Agle topic: Dice / cube.