(i) Let the fraction be yx​Given, y−1x+1​=1x+1=y−1x−y=−2     .....(1)Also,y+1x​=21​2x=y+12x−y=1        .....(2)Substracting (1) from (2)x=3Substituting value of x in (2), 6−y=1y=5Hence, the fraction is 53​(ii) Let the age of Nuri be x and that of Sonu be y.Given, (x−5)=3(y−5)3y−x=10    ..... (1)And,(x+10)=2(y+10)2y−x=−10    ....(2)Subtracting (2) from (1), we gety=20Substituting value of y in (1)60−x=10x=50Hence, the ages of Nuri and Sonu are 50 and 20 respectively.(iii) Let the two digit number be  10x+yGiven, x+y=9         .....(1)And, 9(10x+y)=2(10y+x)90x+9y=20y+2x88x−11y=0           .....(2)Multiplying (1) by 11, we get11x+11y=99       ....(3)Adding (1) and (3)99x=99x=1Substituting this value of x in (1),1+y=9y=8Hence, the number is 18.(iv) Let the number of Rs 100 notes be x and the number of Rs 50 notes be y.Given,x+y=25     ...(1)And, 100x+50y=2000   ...(2)Multiplying (1) by 50, we get50x+50y=1250     ....(3)Subtracting (3) from (2), 50x=750x=15Substituting value of x in (1), 15+y=25y=10(v) Let the fixed charge for first 3days be  Rsx and after 3days the charge for each day be  Rsy.Given, x+4y=27       ....(1) [first 3days + 4days]And,x+2y=21       ...(2) [first 3days + 2days]Subtracting (2) from (1), we get2y=6y=3Substituting value of y in (1)x+4×3=27x+12=27x=15Hence, the fixed charge is Rs 15 and the per day charge is Rs 3.