Two equal sums of money are lent at the same time at 8% and 7% per annum simple interest. The former is recovered 6 months earlier than the latter and the amount in each case is Rs. 2560. The sum and the time for which the sums of money are lent out are.
A. Rs. 2000, 3.5 years and 4 years
B. Rs. 1500, 3.5 years and 4 years
C. Rs. 2000, 4 years and 5.5 years
D. Rs. 3000, 4 years and 4.5 years
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let each sum}} = {\text{Rs}}{\text{. }}x. \cr & {\text{Let the first sum be invested for}} \cr & \left( {T - \frac{1}{2}} \right){\text{years and}} \cr & {\text{the second sum for }}T{\text{ years}}{\text{.}} \cr & {\text{Then,}} \cr & x + \frac{{x \times 8 \times \left( {T - \frac{1}{2}} \right)}}{{100}} = 2560 \cr & \Rightarrow 100x + 8xT - 4x = 256000 \cr & \Rightarrow 96x + 8xT = 256000....(i) \cr & {\text{And,}} \cr & x + \frac{{x \times 7 \times T}}{{100}} = 2560 \cr & \Rightarrow 100x + 7xT = 256000....(ii) \cr & {\text{From(i) and (ii), we get:}} \cr & 96x + 8xT = 100x + 7xT \cr & \Rightarrow 4x = xT \cr & \Rightarrow T = 4 \cr & {\text{Putting }}T = {\text{4 in (i),we get:}} \cr & 96x + 32x = 256000 \cr & \Rightarrow 128x = 256000 \cr & \Rightarrow x = 2000 \cr & {\text{Hence,}} \cr & {\text{each sum}} = {\text{Rs}}{\text{. 2000}} \cr & {\text{time periods}} = \cr & {\text{4 years and }}3\frac{1}{2}{\text{years}} \cr} $$Join The Discussion
Comments ( 2 )
Related Questions on Interest
Find the simple interest on Rs. 5200 for 2 years at 6% per annum.
A. Rs. 450
B. Rs. 524
C. Rs. 600
D. Rs. 624
Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.
A. Rs. 1380
B. Rs. 1290
C. Rs. 1470
D. Rs.1200
E. Rs. 1240
Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.
A. 8%
B. 9%
C. 10%
D. 11%
E. 12%
Rs. 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.
A. Rs. 2300
B. Rs. 2315.25
C. Rs. 2310
D. Rs. 2320
E. None of these
SI is same and P is fix... So R and T inversely proportional to each other.
r t
8/7 7/8 1=1/2 year
8=4years , 7=3.5 years
Let P =100 @ 7% for 4 years = 128
And 128= ₹2560 ,
therefore 1= 20
so, 100 that is principle = ₹20000
Need Smart Approach