1. 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
Explanation:
$$\eqalign{ & {\text{Let each sum}} = {\text{Rs}}{\text{. }}x. \cr & {\text{Let the first sum be invested for}} \cr & \left( {T - \frac{1}{2}} \right){\text{years and}} \cr & {\text{the second sum for }}T{\text{ years}}{\text{.}} \cr & x + \frac{{x \times 8 \times \left( {T - \frac{1}{2}} \right)}}{{100}} = 2560 \cr & 100x + 8xT - 4x = 256000 \cr & 96x + 8xT = 256000....(i) \cr & {\text{And,}} \cr & x + \frac{{x \times 7 \times T}}{{100}} = 2560 \cr & 100x + 7xT = 256000....(ii) \cr & {\text{From(i) and (ii),}} \cr & 96x + 8xT = 100x + 7xT \cr & 4x = xT \cr & T = 4 \cr & {\text{Putting }}T = {\text{4 in (i),}} \cr & 96x + 32x = 256000 \cr & 128x = 256000 \cr & x = 2000 \cr & {\text{each sum}} = {\text{Rs}}{\text{. 2000}} \cr & {\text{time periods}} = \cr & {\text{4 years and }}3\frac{1}{2}{\text{years}} \cr} $$
2. A sum of Rs. 7930 is divided into 3 parts and given at loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then the A received a loan of = ?
a) Rs. 2800
b) Rs. 3050
c) Rs. 2750
d) Rs. 2760
Explanation:
$${\text{A}} + \left( {\frac{{{\text{A}} \times {\text{5}} \times {\text{2}}}}{{{\text{100}}}}} \right) = $$ $${\text{B}} + \left( {\frac{{{\text{B}} \times {\text{5}} \times {\text{3}}}}{{{\text{100}}}}} \right) = $$ $${\text{C}} + \left( {\frac{{{\text{C}} \times {\text{5}} \times {\text{4}}}}{{{\text{100}}}}} \right)$$
110A = 115B = 120C
22A = 23B = 24X
Ratio of amount ( by using L.C.M. of 22, 23 and 24)
$$\eqalign{ & {\text{276 : 264 : 253}} \cr & {\text{A's loan = }}\frac{{276}}{{793}} \times {\text{7930}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 2760}} \cr} $$
3. The principal which gives Rs 1 interest per day at a rate of 5% simple interest per annum is =
a) Rs. 5000
b) Rs. 35500
c) Rs. 7300
d) Rs. 3650
Explanation:
$$\eqalign{ & {\text{Interest = Rs}}{\text{. 1 per day}} \cr & {\text{Interest in one year}} \cr & {\text{ = 1}} \times {\text{365 = Rs}}{\text{. 365}} \cr & {\text{S}}{\text{.I}}{\text{. = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}} \cr & \Rightarrow 365 = \frac{{{\text{P}} \times 5 \times 1}}{{100}} \cr & \Rightarrow {\text{P}} = \frac{{365 \times 100}}{5} \cr & {\text{P}} = {\text{Rs}}{\text{. 7300}} \cr} $$
4. Arvind deposited a sum of money with a bank on 1st january, 2012 at 8% simple interest per annum. He received an amount 3144 on 7th August, 2012. The money he deposited with the bank was = ?
a) Rs. 3080
b) Rs. 2500
c) Rs. 3000
d) Rs. 3100
Explanation:
$$\eqalign{ & {\text{Amount = Rs}}{\text{. 3144}} \cr & {\text{Rate = 8}}\% \cr & {\text{Let, Principal = Rs}}{\text{. }}x \cr & {\text{Time = }} \cr & \frac{{30 + 29 + 31 + 30 + 31 + 30 + 31 + 7}}{{366}} \cr & = \frac{{219}}{{366}} \cr & {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr & \Rightarrow 3144 - x = \frac{{x \times 8 \times 219}}{{100 \times 366}} \cr & = {\text{Rs}}{\text{. 3000}} \cr} $$
5. A man invested Rs. 5000 at some rate of simple interest and Rs. 4000 at 1 percent higher rate of interest. If the interest in both the cases after 4 years is same, the rate of interest in the former case is
a) 4% p.a.
b) 5% p.a.
c) $$6\frac{1}{4}$$ % p.a.
d) $$8\frac{1}{3}$$ % p.a.
Explanation: Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a.
$$\eqalign{ & 5000 \times {\text{R}} \times 4 = 4000 \times \left( {{\text{R}} + 1} \right) \times 4 \cr & \frac{{{\text{R}} + 1}}{{\text{R}}} = \frac{{5000 \times 4}}{{4000 \times 4}} \cr & 1 + \frac{1}{{\text{R}}} = 1 + \frac{1}{4} \cr & {\text{R}} = 4 \cr & {\text{Required rate}} = 4\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$
6. Rahul borrowed a sum of Rs. 1150 from Amit at the simple interest rate of 6 p.c.p.a. for 3 Years. He then added some more money to the borrowed sum and lent it to Sachin for the same time at 9 p.c.p.a simple interest. If Rahul gains Rs. 274.95 by way of interest on borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Sachin ?
a) Rs. 1200
b) Rs. 1285
c) Rs. 1690
d) Rs. 1785
Explanation: Let the money added by Rahul be Rs. x
$$ \frac{{\left( {1150 + x} \right) \times 9 \times 3}}{{100}} - $$ $$\frac{{1150 \times 6 \times 3}}{{100}} = $$ $$274.95$$
1150 × 27 + 27x - 1150 × 18 = 27495
27x + 1150 × (27 - 18) = 27495
27x = 27495 - 10350
27x = 17145
x = 635
So, sum lent by Rahul to Sachin
= Rs. ( 1150 + 635 )
= Rs. 1785
7. The amount Rs. 2100 become Rs. 2352 in 2 years at simple interest. If the interest rate is decreased by 1% , what is the new interest ?
a) Rs. 210
b) Rs. 220
c) Rs. 242
d) Rs. 252
Explanation:
$$\eqalign{ & {\text{Principal}} = {\text{Rs}}{\text{. }}2100 \cr & {\text{Amount}} = {\text{Rs}}{\text{. }}2352 \cr & {\text{SI}} = {\text{A}} - {\text{P}} \cr & \,\,\,\,\,\,\, = 2352 - 2100 \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}252 \cr & {\text{Time = 2 years,}} \cr & {\text{Let rate = R% }} \cr & {\text{R = }}\frac{{252}}{{2100}} \times \frac{{100}}{2}{\text{ = 6% }} \cr & {\text{New rate of interest}} \cr & {\text{ = (6}} - {\text{1)}} \cr & {\text{ = 5% }} \cr & {\text{New interest}} \cr & {\text{ = }}\frac{{2100 \times 5 \times 2}}{{100}} \cr & {\text{ = Rs}}{\text{. 210}} \cr & {\text{Required interest}} \cr & {\text{ = Rs}}{\text{. 210}} \cr} $$
8. Ram deposited a certain sum of money in a company at 12% per annum simple interest for 4 years and deposited equal amounts in fixed deposit in a bank for 5 years at 15% per annum simple interest. If the difference in the interest from two sources is Rs. 1350 then the sum deposited in each case is = ?
a) Rs. 3000
b) Rs. 4000
c) Rs. 6500
d) Rs. 5000
Explanation: Difference between their rates he gained from both boys
$$\eqalign{ & \Rightarrow (15 \times 5)\% - (12 \times 4)\% \cr & \Rightarrow 75\% - 48\% \cr & 27\% = 1350{\text{ }}({\text{given)}} \cr & 100\% = {\text{Rs}}{\text{. 5000}} \cr} $$
9. A some of money lent out at simple interest amount to Rs. 720 after 2 years and Rs. 1020 after a further period of 5 years. Find the principal ?
a) Rs. 6000
b) Rs. 600
c) Rs. 1740
d) Rs. 120
Explanation: Principal + SI for 2 year = Rs. 720 ....(i)
Principal + SI for 7 year = Rs. 1020 ....(ii)
Subtracting equation (i) from (ii)
SI for 5 years = (1020 - 720) = Rs. 300
SI for 1 years = Rs. 60
SI for 2 years = 60 × 2 = Rs. 120
Principal amount = (Amount after 2 years - 2 years SI) = (720 - 120)
Principal amount = Rs. 600
10. A person invested some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested,he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest ?
a) Rs. 400
b) Rs. 500
c) Rs. 700
d) Rs. 800
Explanation: Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y
$$\eqalign{ & 12\% \,{\text{of }}x + 10\% \,{\text{of }}y = 130 \cr & 12x + 10y = 13000 \cr & 6x + 5y = 6500....{\text{(i)}} \cr & {\text{And,}} \cr & 10\% \,{\text{of }}x + 12\% \,{\text{of }}y = 134 \cr & 10x + 12y = 13400 \cr & 5x + 6y = 6700....{\text{(ii)}} \cr & {\text{Adding (i) and (ii), }} \cr & 11\left( {x + y} \right) = 13200 \cr & x + y = 1200.....({\text{iii}}) \cr & {\text{Subtracting (i) from (ii),}} \cr & - x + y = 200.....({\text{iv}}) \cr & {\text{Adding (iii) and (iv), }} \cr & 2y = 1400\,or\,y = 700 \cr & {\text{Amount invested at 12%}} \cr & = \left( {1200 - 700} \right) \cr & = {\text{Rs}}{\text{. 500}} \cr} $$