16. A sum of 44,200 is divided between Johnand Smith, 12 years and 14

1.	16. A sum of 44,200 is divided between Johnand Smith, 12 years and 14 years oldrespectively, in such a way that if theirportions be invested at 10 percent per annumcompound interest, they will receive equalamounts on reaching 16 years of age.(1) What is the share of each out of44,200 ?(ii) What will each receive, when 16 yearsold ?
Answer» Let John's share be x & Smith's share be 44200-x : John's time =16 -12 = 4yrs Smith's time = 16-14 = 2yrs According to the question ; John's amount =Smith's amount x(1+(10/100))4 =(44200 -x)(1+ (10/ 100))2 x(11 /10)4 = (44200 -x) (11/10)2 x(11 /10)2 = 44200 - x 121 x / 100 = 44200 - x (121 x/ 100) + x = 44 200221 x / 100 = 44 200 221 x = 44200 * 100 221 x = 44 20 000 x = 44 20 000 / 221 x = 20 000 Hence , John's share = x = Rs 20,000 Smith's share = 44 200 - 20 000 = Rs 24200

16. A sum of 44,200 is divided between Johnand Smith, 12 years and 14 years oldrespectively, in such a way that if theirportions be invested at 10 percent per annumcompound interest, they will receive equalamounts on reaching 16 years of age.(1) What is the share of each out of44,200 ?(ii) What will each receive, when 16 yearsold ?

Answer»

Let John's share be x & Smith's share be 44200-x :

John's time =16 -12 = 4yrs

Smith's time = 16-14 = 2yrs

According to the question ;

John's amount =Smith's amount

x(1+(10/100))4 =(44200 -x)(1+ (10/ 100))2

x(11 /10)4 = (44200 -x) (11/10)2

x(11 /10)2 = 44200 - x

121 x / 100 = 44200 - x

(121 x/ 100) + x = 44 200221 x / 100 = 44 200

221 x = 44200 * 100

221 x = 44 20 000

x = 44 20 000 / 221

x = 20 000

Hence ,

John's share = x = Rs 20,000

Smith's share = 44 200 - 20 000 = Rs 24200