type 6 si with ratios Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC CGL Prelim 2002]

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) 8 : 5

b) 5 : 8

c) 16 : 15

d) 31 : 6

Answer: (c)

Using Rule 1
Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ or
S.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

Question : 7 [SSC FCI Asst Grade-III 2012]

Ratio of the principal and the amount after 1 year is 10:12. Then the rate of interest per annum is :

a) 16%

b) 12%

c) 20%

d) 18%

Answer: (c)

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%

Question : 8 [SSC SO 2006]

A person invests money in three different schemes for 6 years, 10 years and 12 years at 10 per cent, 12 per cent and 15 per cent simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is

a) 2 : 3 : 4

b) 6 : 3 : 2

c) 3 : 4 : 2

d) 3 : 4 : 6

Answer: (b)

Using Rule 1,

P1 : P2 : P3 = $1/{r_1t_1} : 1/{r_2t_2} : 1/{r_3t_3}$

= $1/{6 × 10} : 1/{10 × 12} : 1/{12 × 15}$

= $1/60 : 1/120 : 1/180$ = 6 : 3 : 2

Question : 9 [SSC CGL Prelim 2007]

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) 6%

b) 4%

c) 7%

d) 5%

Answer: (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%

Question : 10 [SSC CHSL 2015]

If the ratio of principal and the simple interest for 5 years is 10 : 3, then the rate of interest is :

a) 6%

b) 5%

c) 3%

d) 8%

Answer: (a)

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

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