14:I[5014,["/_next/static/chunks/11d1gk4m2o846.js","/_next/static/chunks/14mrh2-p_w84d.js","/_next/static/chunks/40y9lkvta2o_p.js"],"default"] 15:I[38392,["/_next/static/chunks/11d1gk4m2o846.js","/_next/static/chunks/14mrh2-p_w84d.js","/_next/static/chunks/40y9lkvta2o_p.js"],"PracticeCard"] 17:I[70570,["/_next/static/chunks/11d1gk4m2o846.js","/_next/static/chunks/14mrh2-p_w84d.js","/_next/static/chunks/40y9lkvta2o_p.js"],"ExamAppearanceBadge"] 16:T4ee,

Question: The ratio of investments of A, B, and C is 2 : 3 : 4, and their profit ratio is 1 : 2 : 3. If A invested for 12 months, find for how many months C invested.

Solution:
Let the investments of A, B, and C be:
I_A: I_B: I_C= 2 : 3 : 4

Let the time periods of investment be:
T_A: T_B: T_C= ?

Profit = investment × time,
P_A: P_B: P_C= 1 : 2 : 3

So:
I_A × T_A : I_B × T_B : I_C × T_C = 1 : 2 : 3

Substitute investments in ratio form:
⇒ 2 × 12 : 3 × T_B : 4 × T_C = 1 : 2 : 3
⇒ 24 : 3T_B : 4T_C = 1 : 2 : 3

Find multiplier
Let k be the factor:
⇒ 24 = 1 × k
⇒ k = 24

Then:
3T_B = 2 × k
⇒ 3T_B = 2 × 24
⇒ 3T_B = 48
⇒ T_B = 48/3
⇒ T_B= 16 months

Again,
4T_C = 3 × k
⇒ 4T_C = 3 × 24
⇒ 4T_C = 72
⇒ T_C = 72/4
⇒ T_C = 18 months