Sohit and Rohit have a certain sum of money in the ratio of 17 : 14 and they spend their money on purchasing books in the ratio of 12 : 8. After purchasing books each of them has ₹3,392. Find the amount of money that Sohit initially had.​

Correct option is B

Given:

Sohit and Rohit had money in the ratio 17 : 14

They spent money in the ratio 12 : 8 = 3 : 2

After spending, both are left with ₹3,392

Solution:

Let the initial amounts be:

Sohit: 17k,  Rohit: 14k

Let their expenditures be in the ratio 12 : 8, i.e.,

Sohit spends 12m

Rohit spends 8m

Now, 

For Sohit: 17k - 12m = 3392.........(i)

For Rohit: 14k - 8m = 3392 ..........(ii)

Subtract (ii) from (i):

(17k - 12m) - (14k - 8m) = 0

17k - 12m - 14k + 8m = 0

3k - 4m = 0

3k = 4m

m = $$\frac{3}{4}k$$​​

Substitute m = $$\frac{3}{4}k$$​ into equation (ii):

14k - 8$$\left( \frac{3}{4}k \right)$$​ = 3392

14k - 6k = 3392

8k = 3392

k = $$\frac{3392}{8}$$​ = 424

Now find Sohit’s initial amount:

17k = 17 × 424 = ₹7,208 

Alternate Solution: ​

Income = Expenditure + Saving 

32 unit = 3392 

1 unit = $$\frac{3392}{32} = 106$$ 

Sohit's amount = $$106 \times 68=₹7208$$​​