The price of rice increases by 30%. A family reduced its consumption so that the expenditure of the rice is up only by 10%. If the total consumption of the rice before the price rise was 10 kg per month, then the consumption of rice per month at present (in kg) is:

$8\frac{6}{13}$

Total Initial consumption of rice = 10 kg/month

Initial Price = P

Total Exp = 10P

Say they reduced their consumption by x kg/month

Reduced Consumption = (10-x) kg/month

New 30% raised Price = 1.3P

New Exp = 1.3P*(10-x)

Given New Exp is only 10% more than initial exp, 1.3P*(10-x) = 1.1*10P

13P-1.3Px = 11P

2P = 1.3Px

x = 20/13

Total new consumption = 10-x = 10- 20/13 = 110/13

The correct answer is Option (3) → $8\frac{6}{13}$