32. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(a) ₹ 35
(b) ₹ 350
(c) ₹ 245
(d) Can’t be determined
(e) None of these
Solution: (d)
In this type of problems, we use the simple interest formula to find an equation with the given and by using the simple interest formula again for the rate of interest which is increased, we will get another equation. By solving these equations, we will get the required answer. We should have at least two of these terms known along with the simple interest to find the third term.
So, it is impossible to find the interest of RHS without the Principal amount upon solving. So, the answer – can’t be determined.
32. What sum of money must be given as simple interest for six months at 4% per annum in order to earn 150 interest
(a) 5000
(b) 7500
(c) 10000
(d) 15000
(e) 20000
Solution: (b)
P = \(\displaystyle \frac{{150\times 100}}{4}\times \frac{2}{1}=7500\)
33. The rates of simple interest in two banks x and y are in the ratio of 10 : 8. Rajini wants to deposit her total savings in two banks in such a way that she receives equal half-yearly interest from both. She should deposit the savings in banks x and y in the ratio of
(a) 4 : 5
(b) 3 : 5
(c) 5 : 4
(d) 2 : 1
(e) None of these
Solution: (a)
Let the savings be P and Q and rates of SI be 10x and 8x, respectively.
Then,
\(\displaystyle \begin{array}{l}P\times 10x\times \frac{1}{2}\times \frac{1}{{100}}=Q\times 8x\times \frac{1}{2}\times \frac{1}{{100}}\\\Rightarrow 10P=8Q\\\Rightarrow 5P=4Q\\\Rightarrow P:Q=4:5\end{array}\)
34. Find the simple interest on Rs 3000 at 25/4% per annum for the period from 4th Feb 2005 to 18th April 2005.
(a) Rs 45.70
(b) Rs 34.65
(c) Rs 38.50
(d) Rs 37.50
(e) None of these
Solution: (d)
Total Time = (24 + 31 + 18) days = 73 days
(The day on which money is deposited is not counted while the day on which money is withdrawn is counted.)
73 days = \(\displaystyle \frac{{73}}{{365}}\) year= \(\displaystyle \frac{1}{5}\)year
Given,
P=3000, Rate of Interest=25/4%, Time=1/5year
So,
SI=PRT/100= \(\displaystyle 3000\times \frac{{25}}{4}\times \frac{1}{5}\times \frac{1}{{100}}=37.50\)
35. A lent 5000 to B for 2 years and 3000 to C for 4 years on simple interest at the same rate of interest and received 2200 in all from both as interest. The rate of interest per annum is
(a) 7%
(b) 5%
(c) \(\displaystyle 7\frac{1}{8}\%\)
(d) 10%
(e) 12%
Solution: (d)
Let the rate of interest per annum be r%
According to the question,
\(\displaystyle \frac{{5000\times 2\times R}}{{100}}+\frac{{3000\times 4\times R}}{{100}}=2200\)
\(\displaystyle \Rightarrow \)100r + 120r = 2200
\(\displaystyle \Rightarrow \)220 r = 2200
\(\displaystyle \Rightarrow \) r = \(\displaystyle \frac{{2200}}{{220}}=10\%\)
36. A sum of money lent at simple interest amounts to 880 in 2 years and to 920 in 3 years. The sum of money (in rupees) is
(a) 700
(b) 760
(c) 784
(d) 800
(e) 820
Solution: (d)
If the principal be x and rate of interest be r% per annum,
Then SI after 1 year = 920 – 880 = ₹ 40
Therefore, SI after 2 years =₹ 80
\(\displaystyle \Rightarrow \)880 = x + 80
\(\displaystyle \Rightarrow \) x =₹ (880 – 80) =₹ 800
Alternate method:
P = \(\displaystyle (\frac{{{{A}_{2}}{{T}_{1}}-{{A}_{1}}{{T}_{2}}}}{{{{T}_{1}}-{{T}_{2}}}})\)
= \(\displaystyle (\frac{{920\times 2-880\times 3}}{{2-3}})\)
= \(\displaystyle (\frac{{1840-2640}}{{-1}})\)
= \(\displaystyle \frac{{-800}}{{-1}}=800\)
37. What sum of money will amount to ₹ 520 in 5 years and to ₹ 568 in 7 years at simple interest?
(a) ₹ 400
(b) ₹ 120
(c) ₹ 510
(d) ₹ 220
(e) ₹ 280
Solution: (a)
Simple interest for 2 years
=₹ (568 – 520) = ₹ 48
Therefore, Interest for 5 years = \(\displaystyle \frac{{48}}{2}\times 5=120\)
Principal = ₹ (520 – 120) = ₹ 400
Alternate method :
P = \(\displaystyle \frac{{{{A}_{2}}{{T}_{1}}-{{A}_{1}}{{T}_{2}}}}{{{{T}_{1}}-{{T}_{2}}}}\)
= \(\displaystyle \frac{{568\times 5-520\times 7}}{{5-7}}\)
= \(\displaystyle \frac{{2840-3640}}{{-2}}\)
= \(\displaystyle \frac{{-800}}{{-2}}=400\)
38. ₹ 500 was invested at 12% per annum simple interest and a certain sum of money invested at 10% per annum simple interest. If the sum of the interest on both the sum after 4 years is ₹ 480, the latter sum of money is :
(a) ₹ 450
(b) ₹ 750
(c) ₹ 600
(d) ₹ 550
(e) ₹ 650
Solution: (c)
Simple interest gained from 500
\(\displaystyle \frac{{500\times 12\times 4}}{{100}}=240\)
Let the other Principal be x.
S.I. gained = ₹ (480 – 240)
= ₹ 240
\(\displaystyle \frac{{x\times 10\times 4}}{{100}}=240\)
\(\displaystyle \Rightarrow \) x = \(\displaystyle \frac{{240\times 100}}{{40}}=600\)
39. A money lender finds that due to fall in the annual rate of interest 8% to \(\displaystyle 7\frac{3}{4}\%\) his yearly income diminishes by ₹ 61.50. His capital is
(a) ₹ 22400
(b) ₹ 23800
(c) ₹ 24600
(d) ₹ 26000
(e) ₹ 25000
Solution: (c)
Difference in rate = \(\displaystyle (8-7\frac{3}{4})\%=\frac{1}{4}\%\)
Let the capital be ₹ x.
\(\displaystyle \frac{1}{4}\%ofx=61.50\)
\(\displaystyle \Rightarrow \) x = 61.50 × 100 × 4
= ₹ 24600
40. A lends ₹ 2500 to B and a certain sum to C at the same time at 7% annual simple interest. If after 4 years, A altogether receives ₹ 1120 as interest from B and C, the sum lent to C is
(a) 700
(b) 6500
(c) 4000
(d) 1500
(e) 2500
Solution: (d)
Let the sum lent to C be x
According to the question,
\(\displaystyle \frac{{2500\times 7\times 4}}{{100}}+\frac{{x\times 7\times 4}}{{100}}=1120\)
or 2500 × 28 + 28x = 112000
or 2500 + x = 4000
or x = 4000 – 2500 = 1500
