Explanation:

Let the man invests Rs.x at 6% and Rs.y at 7%
Simple Interest on Rs.x at 6% for 2 years + Simple Interest on Rs.y at 7% for 2 years = Rs.354

x×6×2/100 + y×7×2/100 = 354

x×6×2  +y×7×2=  354×100 

x×6 + y×7 = 177×100 

6x + 7y = 17700.........i

One-forth of the first sum is equal to one-fifth of the second sum
= x/4 = y/5

= x = 4y /5..........ii

Solving (1) and (2),

6x+7y = 17700

6(4y/5)+7y = 17700

24y+35y = 17700×5

59y = 17700×5

y = 300×5 = 1500

x=4y/5 = 4×1500/5

= 4×300 = 1200

total sum invested = x + y = 1500 + 1200 = 2700

Hence, option 2 is the correct answer.