Directions (74-78): Study the information carefully and answer the questions given below.

Ten persons were born in five different months of the same year starting from August to December, but on two different dates, i.e., 10th and 15th. K was born in the month which has odd number of days. Six persons were born in between K and D who was born after K. D was not born in the last. Two persons were born between D and S. The number of persons born before S is same as the number of persons born after G. R was born on an even number date and the month which has even number of days. Five persons were born between R and F who was born in the same month as P. Z was born before V but after H.

Who among the following was born on 15th September?

Correct Answer: Z (Option Z)

Step-by-Step Explanation:

Let's analyze the given information step-by-step to arrange the ten persons according to their date of birth.

1. Understanding the Given Dates and Months:

The 5 months (August to December) with 2 dates each (10th and 15th) give 10 possible slots:

1. August 10th (31 days)

2. August 15th (31 days)

3. September 10th (30 days)

4. September 15th (30 days)

5. October 10th (31 days)

6. October 15th (31 days)

7. November 10th (30 days)

8. November 15th (30 days)

9. December 10th (31 days)

10. December 15th (31 days)

2. Determining Positions of K, D, S, and G:

• K was born in a month with an odd number of days (31 days: August, October, December).

• D was born after K, with six persons born between K and D.

• D was not born in the last slot (Dec 15th).

• Therefore, K must be born on August 10th (Slot 1), and D must be born on November 10th (Slot 7, exactly 6 slots after K).

• Two persons were born between D (Slot 7) and S. Moving backwards by 2 persons puts S at Slot 4 (September 15th).

• The number of persons born before S is 3. Thus, the number of persons born after G must also be 3, placing G at Slot 7? No, Slot 10 - 3 = Slot 7, which is occupied by D. So counting from the end: 3 persons after G means G is at Slot 7 (10th - 3 = 7th position from start, i.e., 3 before end is slot 7, wait: 3 born before S (Slots 1, 2, 3) means 3 born after G (Slots 8, 9, 10), so G is at Slot 7 (Nov 10th)? But D is at Slot 7! Let's check: 3 persons before S (August 10, August 15, September 10). So 3 persons after G means G is born on November 10th? Wait, let's recount slots: 1(Aug 10), 2(Aug 15), 3(Sep 10), 4(Sep 15 - S), 5(Oct 10), 6(Oct 15), 7(Nov 10 - D), 8(Nov 15), 9(Dec 10), 10(Dec 15). Persons born before S: 3 (slots 1, 2, 3). Persons born after G must be 3 (slots 8, 9, 10). So G is at slot 7. But D is at slot 7. Let's re-verify K's position:

If K is August 15th (Slot 2), 6 persons between K and D means D is at Slot 9 (December 10th). D is not born in the last (Slot 10 is Dec 15th, so Dec 10th is fine!).

Let's check this case (K on Aug 15th):

• K = August 15th (Slot 2)

• 6 persons between K and D → D = December 10th (Slot 9)

• Two persons between D (Slot 9) and S → S = October 15th (Slot 6)

• Persons before S (Slot 6) = 5 (Slots 1, 2, 3, 4, 5). So persons after G must also be 5 (Slots 6, 7, 8, 9, 10), which places G at Slot 5 (October 10th).

3. Determining R, F, and P:

• R was born on an even number date (10th) and in a month with an even number of days (30 days: September or November).

• So R is either on September 10th (Slot 3) or November 10th (Slot 7).

• Five persons between R and F, who was born in the same month as P.

• If R is November 10th (Slot 7): 5 persons before R puts F at Slot 1 (August 10th). P must be in the same month as F, so P is August 15th, but K is already at August 15th! Contradiction.

• Thus, R must be on September 10th (Slot 3). 5 persons after R puts F at Slot 9? No, Slot 3 + 5 + 1 = Slot 9, which is occupied by D. 5 persons before R is not possible (only 2 slots). So 5 persons between Slot 3 and F puts F at Slot 9? Wait, between slot 3 and slot 9 there are 5 slots (4, 5, 6, 7, 8). So F is at Slot 9? But D is at Slot 9! Wait, let's re-check 5 persons between R and F:

Slot 3 (R) + 5 persons + F = Slot 9 (D). Can F be at Slot 9? No, D is at Slot 9!

Wait, let's re-verify: What if K is at August 10th (Slot 1)?

If K = August 10th (Slot 1), D = November 10th (Slot 7). Two between D and S → S = August 15th (Slot 2) or November 15th (Slot 8)?

Let's test S = August 15th (Slot 2):

• Persons before S (Slot 2) = 1. Persons after G = 1 → G = December 10th (Slot 9).

• R on even date + even month (Sep 10 = Slot 3 or Nov 10 = Slot 7). Since Slot 7 is D, R must be September 10th (Slot 3).

• Five persons between R (Slot 3) and F → F = December 15th (Slot 10).

• F is born in the same month as P → P = December 10th, but G is at Dec 10th! Contradiction.

What if S = November 15th (Slot 8)?

• Persons before S (Slot 8) = 7. Persons after G = 7 → G = September 10th (Slot 3).

• R on even date + even month → R must be November 10th? No, D is at Nov 10th (Slot 7). So R cannot be Nov 10th or Sep 10th (G is at Sep 10th)!

Wait! Is there another month with odd number of days? October (31 days)!

If K is October 10th (Slot 5), D would be after 6 persons, which is out of range.

Let's re-examine R on Nov 10th when K = Aug 15th (Slot 2), D = Dec 10th (Slot 9), S = Oct 15th (Slot 6), G = Oct 10th (Slot 5):

• R is at November 10th (Slot 7). 5 persons between R (Slot 7) and F → F is at Slot 1 (August 10th).

• F is in the same month as P (August). Since Slot 1 is F and Slot 2 is K, P is not in August? Wait! K was born in August 15th! So P cannot be in August! Contradiction.

Wait! What if R is September 10th (Slot 3)? Five persons between R (Slot 3) and F (Slot 9)? But D is at Dec 10 (Slot 9)! Wait! Slot 3 to 9: 4, 5, 6, 7, 8 are 5 persons! So F would be at Slot 9! But D is at Slot 9! What if F is at Slot 10 (Dec 15th)? Then between Slot 3 and Slot 10 there are 6 persons (4, 5, 6, 7, 8, 9)!

Let's check if K = August 10th, D = November 15th? No, "six persons were born in between K and D", so if K is Slot 1, D is Slot 8 (Nov 15th).

Let's test K = Slot 1 (Aug 10th), D = Slot 8 (Nov 15th):

• 6 persons between K (1) and D (8): 2, 3, 4, 5, 6, 7 (6 persons!). Perfect!

• D was not born in the last (Slot 10), so Nov 15th (Slot 8) is valid!

• Two persons between D (8) and S → S = October 15th (Slot 6) [7, 6 are 2 persons between? No, 7 and 6: wait, between 8 and 5 there are 6 and 7 (2 persons)]. So S = October 10th (Slot 5).

• Persons before S (Slot 5) = 4 (Slots 1, 2, 3, 4). Persons after G = 4 → G = October 15th (Slot 6) [Slots 7, 8, 9, 10 are 4 persons after G].

• R born on even date & even month (Sep 10 = Slot 3 or Nov 10 = Slot 7).

• If R = Nov 10th (Slot 7): 5 persons between R (7) and F → F = Aug 15th (Slot 2) [Slots 6, 5, 4, 3, 2 are 5 persons between? No, between 7 and 1 are 2, 3, 4, 5, 6 (5 persons!). So F = Aug 10th? But K is at Aug 10th].

• If R = Sep 10th (Slot 3): 5 persons between R (3) and F → F = Nov 10th (Slot 7) [Slots 4, 5, 6 are 3 persons? Between 3 and 9: 4, 5, 6, 7, 8 are 5 persons, so F = Dec 10th (Slot 9)].

• F = Dec 10th (Slot 9). F and P are in the same month (December) → P = Dec 15th (Slot 10).

Let's verify remaining positions for H, Z, V:

• Remaining empty slots are: Slot 2 (Aug 15th) and Slot 4 (Sep 15th).

• Given: "Z was born before V but after H".

• So the order is H → Z → V.

• Since H is before Z and Z is before V, H must be at Slot 2 (Aug 15th), Z must be at Slot 4 (September 15th), and V can be at another position if available, but here Z falls directly on Slot 4 (September 15th)!

Final Schedule Table:

• August 10th: K

• August 15th: H

• September 10th: R

• September 15th: Z

• October 10th: S

• October 15th: G

• November 10th: (Remaining slot for V)

• November 15th: D

• December 10th: F

• December 15th: P

Therefore, Z was born on 15th September.