Option 2 : 104

**Given:**

Four partners A, B, C and D invested 75000, 55000, 80000 and 125000 respectively.

Investment of A is for 4 months more than that of B

Investment of C is for 6 months more than that of D

**Formula Used:**

Ratio of Profit = Ratios of product of Amount invested and time

**Calculation:**

Let B and D invested for 2x and 3x months respectively.

According to the question,

Time period of A and C is (2x + 4) and (3x + 6) months respectively.

Now,

Ratio of profits of A, B, C and D

A : B : C : D = 75000 × (2x + 4) : 55000 × 2x : 80000 × (3x + 6) : 125000 × 3x

⇒ 15 × (2x + 4) : 11 × 2x : 16 × (3x + 6) : 25 × 3x

⇒ (30x + 60) : 22x : (48x + 96) : 75x

⇒ (30x + 60) + 22x + (48x + 96) + 75x

⇒ 175x + 156 = 8906

⇒ 175x = 8750

⇒ x = 50

∴ A invested for 2x + 4 = 2 × 50 + 4 = 104 months