Practice Si with ratios - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years, with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest is
(a)
(b)
(c)
(d)
Using Rule 1,
Case-I,
Interest = 5x - 4x = x
$x = {4x × R × T}/100$
T = $25/R$ years
Case-II,
T = $25/R + 3 = ({25 + 3R}/R)$ years
SI = 7 y - 5y = 2y
$2y = {5y × R × (25 + 3R)}/{R × 100}$
40 = 25 + 3R
3R = 40 –25 = 15 %
R = $15/3$ = 5%
Q-2) If the ratio of principal and the simple interest for 5 years is 10 : 3, then the rate of interest is :
(a)
(b)
(c)
(d)
Using Rule 1,
$\text"Principal"/ \text"Interest" = 10/3$
$\text"Interest"/ \text"Principal" = 3/10$
Rate = $\text"S.I. × 100"/ \text"Principal × Time"$
= $3/10 × 100/5$ = 6% per annum
Q-3) Ratio of the principal and the amount after 1 year is 10:12. Then the rate of interest per annum is :
(a)
(b)
(c)
(d)
Using Rule 1,
$\text"Principal"/\text"Amount" = 10/12$
$\text"Amount"/ \text"Principal" = \text"Principal + interest"/ \text"Principal" = 12/10$
1 + $\text"Interest"/ \text"Principal" = 12/10$
$\text"Interest"/ \text"Principal" = 2/10 = 1/5$
Rate = $1/5$ × 100 = 20%
Q-4) If ratio of principal and simple interest for 1 year is 25 : 1, then the rate of interest is
(a)
(b)
(c)
(d)
Using Rule 1,
Principal : Interest = 25 : 1
Interest : Principal = 1 : 25
Rate = $\text"S.I. × 100"/ \text"Principal × Time"$
= $1/25$ × 100 = 4% per annum
Q-5) A person lent Rs.5,000 partly at the rate of 4 per cent and partly at the rate of 5 per cent per annum simple interest. The total interest after 2 years is Rs.440. To find the sum of money lent at each of the above rates, Rs.5,000 is to be divided in the ratio :
(a)
(b)
(c)
(d)
Using Rule 1,
Let the sum of x be lent at the rate of 4% and (5000 - x) at the rate of 5%
${x × 4 × 2}/100 + {(5000 - x) × 5 × 2}/100$ = 440
8x + 50000 - 10x = 44000
2x = 50000 - 44000 = 6000
x = Rs.3000
Rs.(5000 - x) = Rs.(5000 - 3000) = Rs.2000
Now, Required ratio
= 3000 : 2000 = 3 : 2
Q-6) A person borrows some money for 5 years and loan amount : total interest amount is 5 : 2. The ratio of loan amount : interest rate is equal to :
(a)
(b)
(c)
(d)
Required ratio = 5 : $2/5$ = 25 : 2
$\text"loan amount"/ \text"Interest amount" = 5/2$
Interest rate = $2/5$
[Since, ${P + I}/I = 5/2 ⇒ P/I + I = 5/2$
⇒ $P/I = 3/2, then I = 2/5$]
$ \text"loan amount"/ \text"Interest rate"$
= $5/{2/5}= 25/2$ or 25 : 2
Q-7) Rs.12,000 is divided into two parts so that the simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for 4$1/2$ years at 16% per annum. The ratio of the first part to the second part is
(a)
(b)
(c)
(d)
Using Rule 1,
First part = Rs. x and second part
= (12000 - x )
${x × 3 × 12}/100 = {(12000 - x) × 9 × 16}/200$
$x/{12000 - x} = {9 × 16 × 100}/{3 × 12 × 200}$
= $2/1$ = 2 : 1
Q-8) A sum of Rs.1550 was lent partly at 5% and partly at 8% simple interest. The total interest received after 3 years is Rs.300. The ratio of money lent at 5% to that at 8% is :
(a)
(b)
(c)
(d)
Using Rule 1Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ orS.I. = ${\text"P × R × T"/100$P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$ A = P + S.I. or S.I. = A - P
Let the sum lent at the rate of interest 5% per annum is x and at the rate of interest 8% per annum is (1550 - x)
According to the question,
${x × 5 × 3}/100 + {(1550 - x) × 8 × 3}/100$ = 300
${15x}/100 + {37200 - 24x}/100$ = 300
15x + 37200 - 24x = 300 × 100
9x = 7200
x = Rs.800 and,
1550 - x = 1550 - 800 = Rs.750
Ratio of money lent at 5% to that at 8%
= 800 : 750 = 16 : 15
Q-9) In a certain time, the ratio of a certain principal and the simple interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years the money was invested is
(a)
(b)
(c)
(d)
Using Rule 1,
Time = $\text"S.I. × 100"/ \text"Principal × Rate"$
= $3/10 × 100/10$ = 3 years
Q-10) A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352, the sum lent at 8% is
(a)
(b)
(c)
(d)
Principal lent at 8% S.I. = Rs.x.
Principal lent at 10% S.I. = Rs.(4000 - x)
S.I. = $\text"Principal × Time × Rate"/100$
${x × 8}/100 + {(4000 - x) × 10}/100$ = 352
8x + 40000 - 10x = 35200
2x = 40000 - 35200 = 4800
x = $4800/2$ = Rs.2400