Kesav gave a total of Rs. 80,000 on interest. He gave half of the total amount on simple interest in that some amount at 8% pa. and the remaining at the 10%pa. And half of the remaining on compound interest in that also some amount for 6% p.a and remaining at 5% p.a. At the end of three years he received total simple interest of Rs. 11,100 and total compound interest of Rs.16,705.69. Find the difference between amount he gave on simple interest at 10% and on compound interest at 5%
Rs. 3200
Rs. 3500
Rs. 3000
Rs. 3700
Answers
- Data is incorrect .
Given :-
- Kesav gave a total of Rs. 80,000 on interest .
- Half of the total amount on simple interest in that some amount at 8% pa. and the remaining at the 10%pa.
- Half of the remaining on compound interest in that also some amount for 6% p.a and remaining at 5% p.a.
- Total simple interest recieved at the end of three years = Rs. 11,100
- Total compound interest recieved at the end of three years = Rs. 116,705.69
To Find :- The difference between amount he gave on simple interest at 10% and on compound interest at 5% ?
Formula used :-
- Simple interest (SI) = (P × R × T)/100
- Compound interest (CI) = P[{1 + (r/100)}^T - 1]
- where P = Principal, R = Rate of interest per annum, T = Time period .
Solution :-
→ Total amount = Rs. 80,000
So,
→ Amount given at SI = Rs. 40,000 { Half }
→ Amount given at CI = Rs. 40,000 { Half }
Case 1) :- Simple interest
Let amount given at 8% pa is equal to Rs.100x .
So,
→ P = Rs. 100x
→ R = 8% pa
→ T = 3 years
→ SI = (P × R × T)/100 = (100x * 8 * 3)/100 = Rs. 24x
and,
→ Principal left = Rs. (40000 - 100x)
→ R = 10% pa
→ T = 3 years
→ SI = (P × R × T)/100 = [100(400 - x) * 10 * 3]/100 = Rs. (12000 - 30x)
given that, total simple interest recieved is equal to Rs. 11,100 .
therefore,
→ 24x + (12000 - 30x) = 11100
→ 12000 - 30x + 24x = 11100
→ 12000 - 6x = 11100
→ 12000 - 11100 = 6x
→ 900 = 6x
→ x = Rs. 150
hence,
→ Amount given at 10% simple interest = (40000 - 100x) = (40000 - 100 × 150) = 40000 - 15000 = Rs. 25000 --------- Equation (1)
Case 2) :- Compound Interest
→ Total amount given in CI = Half of remaining = 40000 ÷ 2 = Rs. 20000
Let us assume that, amount given at 6% p.a is equal to Rs. P .
So,
→ P = Rs. P
→ R = 6% p.a
→ T = 3 years
→ CI = P[{1 + (R/100)}^T - 1] = P[{1 + (6/100)}³ - 1] = P[{1 + (3/50)}³ - 1] = P[(53/50)³ - 1] = Rs. (23877P/125000)
and,
→ Principal left = Rs. (20000 - P)
→ R = 5% p.a
→ T = 3 years
→ CI = P[{1 + (R/100)}^T - 1] = (20000 - P)[{1 + (5/100)}³ - 1] = (20000 - P)[{1 + (1/20)}³ - 1] = (20000 - P)[(21/20)³ - 1] = (20000 - P)(1261/8000) = Rs. [3152.5 - (1261P/8000)]
given that, total CI is equal to Rs. 16705.69
therefore,
→ (23877P/125000) + [3152.5 - (1261P/8000)] = 16705.69
→ (23877P/125000) - (1261P/8000) = 16705.69 - 3152.5
→ (23877P * 8 - 1261P * 125) / 1000000 = 13553.19
→ 191016P - 157625P = 13553.19 * 1000000
→ 33391P = 13553190000
→ P = Rs. 405893.50
As w can see that, P is greater than Rs. 20000 . Therefore, we can conclude that given data is incorrect . Value of total compound interest as Rs.16705.69 is incorrect here . Please check once and put exact value here now .
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Answer:
Step-by-step explanatio37000