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The salary of Mina is тВ╣80,000. Out of which she deposits x% amount at 15% simple interest. If the accumulated amount for the money deposited after 3 years is тВ╣17,400, then find the value of x.
25
12
20
15
15
Calculate the interest factor as (1+0.15├Ч3)=1.45. Divide the final amount 17400 by 1.45 to find the principal P=12000. Then, 12000 is what percentage of 80000: (12000/80000)├Ч100=15.
Total salary = тВ╣80,000, Percentage deposited = x%, Rate of interest (R) = 15%, Time (T) = 3 years, Accumulated Amount (A) = тВ╣17,400.
A=P├Ч(1+100R├ЧTтАЛ)
Calculate the interest factor as (1+0.15├Ч3)=1.45. Divide the final amount 17400 by 1.45 to find the principal P=12000. Then, 12000 is what percentage of 80000: (12000/80000)├Ч100=15.
Students often mistake the total salary тВ╣80,000 for the principal P of the interest calculation, forgetting that only x% of it was deposited.
Define variables
Let the principal amount deposited be P. Since x% of the salary is deposited, P=100xтАЛ├Ч80000=800x.
P=800x
Apply Interest Formula
The accumulated amount A is the sum of principal and simple interest. The formula is A=P(1+100RTтАЛ). Substituting R=15% and T=3 years:
17400=P(1+10015├Ч3тАЛ)=P(1+0.45)=1.45P
Calculate Principal P
Solving for P, we get P=1.4517400тАЛ. Calculating this gives P=12000.
P=12000
Solve for x
Now substitute P=12000 back into the equation 800x=12000. Solving for x gives x=80012000тАЛ=15.
x=15
D is correct because the principal amount deposited is тВ╣12,000, which is exactly 15% of the total salary of тВ╣80,000.
This type of problem frequently appears in competitive exams to test the ability to link percentage distributions with financial math formulas like Simple or Compound Interest.