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

Question : 1 [SSC MTS 2011]

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

Question : 2 [SSC CGL Prelim 2002]

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 : 3 [SSC CGL Tier-II 2016]

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 : 4 [SSC SO 2005]

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

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

Question : 5 [SSC CHSL 2012]

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

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