type 6 si with ratios Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 6 EXERCISES

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The following question based on simple interest topic of quantitative aptitude

Questions : 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) 2 : 1

(b) 2 : 25

(c) 25 : 2

(d) 5 : 2

The correct answers to the above question in:

Answer: (c)

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

Practice simple interest (type 6 si with ratios) Online Quiz

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Read more si with ratios Based Quantitative Aptitude Questions and Answers

Question : 1

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) 1 : 2

b) 2 : 1

c) 3 : 2

d) 2 : 3

Answer: (b)

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

Question : 2

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 : 3

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 : 4

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) Rs.2200

b) Rs.2900

c) Rs.3100

d) Rs.2400

Answer: (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

Question : 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) 3 : 2

b) 4 : 5

c) 2 : 3

d) 5 : 4

Answer: (a)

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

Question : 6

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) 3 years

b) 1 year

c) 7 years

d) 5 years

Answer: (a)

Using Rule 1,

Time = $\text"S.I. × 100"/ \text"Principal × Rate"$

= $3/10 × 100/10$ = 3 years

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