A sum of ₹16,000 is divided between Rahul and Vinod. Rahul invested is sum at 7.5% p.a. for 4 years at simple interest,and Vinod invested is sum at 12% p.a for 4 years simple interest. If the total interest received by Rahul and Vinod together is ₹6,024 then the sum invested by Rahul is:

Let's assume the money invested by Rahul is 'y'.

A sum of ₹16,000 is divided between Rahul and Vinod.

money invested by Vinod = (16000-y)

Rahul invested is sum at 7.5% p.a. for 4 years at simple interest,and Vinod invested is sum at 12% p.a for 4 years simple interest. If the total interest received by Rahul and Vinod together is ₹6,024.

y of 7.5% of 4 + (16000-y) of 12% of 4 = 6024

$$y\times\frac{7.5}{100}\times\ 4+(16000-y)\times\frac{12}{100}\times4=6024$$

$$30y+(16000-y)\times48=602400$$

$$10y+(16000-y)\times16=200800$$

$$10y+256000-16y=200800$$

6y = 55200

y = 9200

Sum invested by Rahul = y = 9200