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The salary of Rahul is тВ╣60,000. Out of which he deposits x% amount at 10% simple interest. If the accumulated amount for the money deposited after 2 years is тВ╣15,600, then find the value of x.
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Given: Rahul's total salary is 60000, deposited amount is x% of 60000, rate of interest is 10%, time period is 2 years, and the final accumulated amount (Principal + Simple Interest) is 15600.
Rahul's total salary is 60000, deposited amount is x% of 60000, rate of interest is 10%, time period is 2 years, and the final accumulated amount (Principal + Simple Interest) is 15600.
A=P(1+100R├ЧTтАЛ)
Use the effective interest rate concept: In 2 years at 10% per annum, the total interest is 2├Ч10=20%. Thus, the total amount is 120% of the principal. Set 1.2P=15600 to find P=13000, then calculate x=(13000/60000)├Ч100.
Students often mistake the given amount 15600 for the Interest instead of the Accumulated Amount (Principal + Interest).
Define the Variables
Let the Principal amount deposited be P. Given P=x%┬аof┬а60000=100xтАЛ├Ч60000=600x. The accumulated amount A is 15600 and Rate R=10% per annum for T=2 years.
P=600x,A=15600,R=10%,T=2
Apply Amount Formula
The formula for the total accumulated amount is A=P+SI, where SI=100P├ЧR├ЧTтАЛ. Substituting the values, we get 15600=P(1+10010├Ч2тАЛ).
15600=P(1+10020тАЛ)=1.2P
Calculate Principal P
Solving for P, we have P=1.215600тАЛ=13000.
P=13000
Find x
Since P=600x, we equate 600x=13000. Thus, x=60013000тАЛ=6130тАЛтЙИ21.67. Wait, let's recheck the calculation. The option provided is 20, which implies 12000 deposited. 1.2├Ч12000=14400. Re-evaluating: if x=20, P=12000, A=14400. If A=15600 and R=10,T=2, then P=13000, x=13000/600=21.66. Given the answer key, there might be a typo in the question's target value.
x=60013000тАЛ=21.67
A is correct because, based on the standard Simple Interest formula, P=13000 and x=21.67, although the official key suggests 20 likely due to a rounding or source discrepancy.
This is a base-level problem for 'Mixture and Alligation' where you balance two different interest rates, which frequently appears in banking exams.