A and B invested in a business in the ratio 5 : 6. The profit ratio was 10 : 9. If B invested his money for 12 months, for how many months did a invest?

Correct option is B

Given :

Investment ratio of A : B = 5 : 6
Profit ratio of A : B = 10 : 9
B invested for 12 months

Formula Used :
​$$\text{Profit} \propto (\text{Investment}) \times (\text{Time})$$​​
Solution :

Time of investment of A = x months

​$$\frac{5 \times x}{6 \times 12} = \frac{10}{9}$$​​

5$$x \times 9 = 10 \times 6 \times 1$$​2

45x = 720

x $$= \frac{720}{45}$$​= 16 months