If rs. 7700 are divided among three brothers anuj, vijay and dhiraj in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 years, respectively remains equal, the share of anuj is more than that of dhiraj by?
Answers
The share of Anuj is more than that of Dhiraj by Rs. 2800.
• Total amount of money to be divided among Anuj, Vijay and Dhiraj = Rs. 7700
Let the share of Anuj be Rs. X, the share of Vijay be Rs. Y, and the share of Dhiraj be Rs. Z.
• Given rate of simple interest per annum for all three = 5 %
Time for Anuj = 1 year
Time for Vijay = 2 years
Time for Dhiraj = 3 years
• The simple interest for a given amount in a given period of time is given as :
Simple Interest = ( Principal × Rate × Time ) / 100
∴ S.I. for Anuj after 1 year = ( X × 5 × 1 ) / 100 = X / 20
S.I. for Vijay after 2 years = (Y × 5 × 2 ) / 100 = Y / 10
S.I. for Dhiraj after 3 years = ( Z × 5 × 3 ) / 100 = 3Z / 20
• According to the question,
X / 20 = Y / 10 = 3Z / 20
Or, X / 20 = 3Z / 20 ; Y / 10 = 3Z / 20
Or, X = (3Z × 20 ) / 20 ; Y = (3Z × 10 ) / 20
Or, X = 3Z - (i) ; Y = 3Z / 2 - (ii)
• Also, according to the question,
X + Y + Z = Rs. 7700
=> 3Z + (3Z / 2) + Z = Rs. 7700 [ substituting X and Y from eq. (i) and (ii)]
=> ( 6Z + 3Z + 2Z ) / 2 = Rs. 7700
=> 11Z = 2 × Rs. 7700
=> Z = ( 2 × Rs. 7700 ) / 11
=> Z = Rs. 1400
Therefore, Dhiraj's share is Rs. 1400.
• Putting the value of Z in eq. (i), we get,
X = 3 × Rs.1400 = Rs. 4200
Therefore, Anuj's share is Rs. 4200.
• Difference between Anuj's share and Dhiraj's share = Rs. 4200 - Rs. 1400 = Rs. 2800
Therefore, Anuj received Rs. 2800 more than Dhiraj.