# Simple Interest Quiz Set 017

### Question 1

A sum of Rs. 24160 is divided into three parts such that simple interest on these parts at 10% p.a. after 11, 18 and 14 years, respectively, is same. What is the amount of the smallest part?

A

Rs. 6160.

B

Rs. 6260.

C

Rs. 6060.

D

Rs. 6360.

Soln.
Ans: a

We should use the shortcut technique here. If r1, t1, r2, t2 and r3, t3 be the rates and times for three parts with same interest amount, then the three parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2} : 1/{r_3 t_3}$. In our case r1 = r2 = r3 = 10, which cancels, so the ratio is $1/t_1 : 1/t_2 : 1/t_3$. The product of denominators is 11 × 18 × 14 = 2772. Thus, the three parts are in the ratio $252 : 154 : 198$. The parts are: 24160 × $198/{252 + 154 + 198}$, 24160 × $154/{252 + 154 + 198}$ and 24160 × $252/{252 + 154 + 198}$, which are 10080, 6160 and 7920. The smaller is Rs. 6160.

### Question 2

The difference between simple interests on an amount @8% for 22 years and at 5% for 17 years is Rs. 182. What is the amount?

A

Rs. 200.

B

Rs. 300.

C

Rs. 250.

D

Rs. 400.

Soln.
Ans: a

The shortcut formula is P = ${\text"diff" × 100}/{r_1 × t_1 - r_2 × t_2}$. Putting r1 = 8, t1 = 22, r2 = 5, t2 = 17, diff = 182, we get P = Rs. 200.

### Question 3

The difference between simple interests on an amount @11% for 18 years and at 6% for 16 years is Rs. 816. What is the amount?

A

Rs. 800.

B

Rs. 900.

C

Rs. 700.

D

Rs. 1000.

Soln.
Ans: a

The shortcut formula is P = ${\text"diff" × 100}/{r_1 × t_1 - r_2 × t_2}$. Putting r1 = 11, t1 = 18, r2 = 6, t2 = 16, diff = 816, we get P = Rs. 800.

### Question 4

A sum of Rs. 270 is divided into two parts such that simple interest on these parts at 10% p.a. after 1 and 2 years, respectively, is same. What is the amount of the smaller part?

A

Rs. 90.

B

Rs. 190.

C

Rs. 140.

D

Rs. 290.

Soln.
Ans: a

We should use the shortcut technique here. If r1, t1, r2, t2 be the rates and times for two parts with same interest amount, then the two parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2}$. In our case r1 = r2 = 10, which cancels, so the ratio is $1/t_1 : 1/t_2$. Thus, the two parts are in the ratio $t_2 : t_1$. The parts are: 270 × $2/{1 + 2}$, and 270 × $1/{1 + 2}$, which are 180 and 90. The smaller is Rs. 90.

### Question 5

A sum of Rs. 1100 is divided into two parts such that simple interest on these parts at 10% p.a. after 6 and 5 years, respectively, is same. What is the amount of the smaller part?

A

Rs. 500.

B

Rs. 600.

C

Rs. 400.

D

Rs. 700.

Soln.
Ans: a

We should use the shortcut technique here. If r1, t1, r2, t2 be the rates and times for two parts with same interest amount, then the two parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2}$. In our case r1 = r2 = 10, which cancels, so the ratio is $1/t_1 : 1/t_2$. Thus, the two parts are in the ratio $t_2 : t_1$. The parts are: 1100 × $5/{6 + 5}$, and 1100 × $6/{6 + 5}$, which are 500 and 600. The smaller is Rs. 500.