Profit and Loss Test

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Profit and Loss Test - 14

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Question 1
1 / -0

A certain sum of money lent on simple interest doubles itself in 10 years. In how many years will it triple itself?

A
20 years

B
25 years

C
30 years

D
15 years

Solution

Let the P = Rs. 100
Amount = Rs. 200
Time = 10 years
Hence, SI = 200 - 100 = Rs. 100
R = = 10%
P = Rs. 100
Amount = Rs. 300
R = 10%
SI = 300 - 100 = Rs. 200
Time = = 20 years
Question 2
1 / -0

Find the minimum number of years for which simple interest must be reckoned at 5% p.a. on Rs. 512.50 so that the interest may be an exact number in rupees.

A
4 years

B
8 years

C
6 years

D
10 years

Solution

Let P = Rs. 512.50
R = 5%
Let Time = x
∴ S.I. =
can be an exact number (minimum) if x = 8.
Therefore, time = 8 years.
Question 3
1 / -0

John borrowed Rs. 3000 from Mohan at a rate of 10% p.a simple interest for 3 years. At the end of the year, he paid the interest for that year and part of the loan, altogether Rs. 800. Similarly, he paid Rs. 800 at the end of the 2^nd year. What sum must he pay now to clear off the debt?

A
Rs. 2145

B
Rs. 2060

C
Rs. 2045

D
Rs. 2100

Solution

Total Amount to be paid In first year = Rs.3300

Remaining amount after paying interest plus part of the loan = 3300- 800 = RS.2500

Now, Total Amount to be paid after second year = Rs.2750 ( P + SI)

Remaining amount after paying interest plus part of the loan = 2750- 800 = Rs.1950

Total amount to be paid off in the 3rd year = 1950 + 10 % SI = Rs. 2145
Question 4
1 / -0

Seema lent a certain sum of money at 12%; and in 7 years, the interest amounted to Rs. 800 less than the sum lent. What was the sum lent?

A
Rs. 5200

B
Rs. 4500

C
Rs. 5000

D
Rs. 6000

Solution

Let sum = x
Interest = (x - 800)
x - 800 =
100x - 80,000 = 84x
100x - 84x = 80,000
16x = 80,000
x = 5000
Question 5
1 / -0

Two equal sums of money were invested at simple interest, one at 3% and the other at 3.5%. At the end of 3 years, the interest received from the latter investment exceeded that received from the former investment by Rs. 120. Find the sum invested.

A
Rs. 8000

B
Rs. 8050

C
Rs. 9000

D
Rs. 9500

Solution

Let sum = x
Rate = 3%
Time = 3 years
S.I. =
2^nd time sum = x
Rate = 3.5%
Time = 3 years
S.I. =
= 120
= 120
x = = Rs.8000
Question 6
1 / -0

Sudhir has Rs. 7000. He lends Rs. 3000 at 5% and Rs. 2000 at 6%. At what rate must he lend the remainder of his money so that his total income may be 8% on Rs. 7000? (Duration of all the lending is 1 year.)

A
6%

B
7%

C
14%

D
%

Solution

Income on Rs. 3000 = = Rs. 150
Income on Rs. 2000 = = Rs. 120
Remainder amount = 7000 - 5000 = Rs. 2000
Income desired = = Rs. 560
Interest required on Rs. 2000 = 560 - (150 + 120) = 560 - 270 = Rs. 290
Rate = = 14%
Question 7
1 / -0

What annual payment will discharge a debt of Rs. 4910 due in 5 years, the rate of interest being 9% per annum?

A
Rs. 832.20

B
Rs. 1100

C
Rs. 900

D
Rs. 1050

Solution

Let Rs. P is the annual payment
The amount of Rs. P for 4 years at 9% =
The amount of Rs. P for 3 years at 9% =
The amount of Rs. P for 2 years at 9% = P
The amount of Rs. P for 1 year at 9% = P
These four amounts and the last annual payments of Rs. P will discharge the debt of Rs.4910
= 4910
= 4910
= 4910
P = = 832.20.
Question 8
1 / -0

A man borrows Rs. 3000 at 6% per annum from B. Each year, he pays Rs. 400 for interest and part payment of the debt. What amount does A owe at the end of 3 years?

A
Rs. 1800

B
Rs. 2299.61

C
Rs. 2200

D
Rs. 2199.60

Solution

Sum = Rs.3000
R = 6%
T = 3 years
SI for 1^st year =
= 180
Amount = 3000 + 180 = 3180
Remaining sum = 3180 - 400
= 2780
SI for 2^nd year = = 166.80
Amount = 2780 + 166.80
= 2946.80
Remaining sum = 2946.80 - 400
= 2546.80
SI for 3^rd year =
= 152.81
= 2546.80 + 152.81
Amount = Rs.2699.61
Hence, amount to be given = 2699.61 - 400 = Rs. 2299.61
Question 9
1 / -0

A and B borrow a total sum of Rs. 30000 from C at 4% p.a. for 5 years and 5% for 4 years, respectively. Find out the sum borrowed by A, if A's interest is double than that of B's interest.

A
Rs. 10000

B
Rs. 20000

C
Rs. 18000

D
Rs. 15000

Solution

Let the sum borrowed by A = Rs. x

Then, the sum borrowed by B = Rs. 30000 - x

Hence, interest of A =

Interest of B = =

Hence, =

x = 60000 - 2x

3x = 60000

x = Rs. 20000
Question 10
1 / -0

Divide Rs. 30,000 into the two sums such that if the first be put out at S.I. for 5 years at p.c; and the second for 4 years at 5%, Interest of the first sum shall be double that of the second. If first part be x & other is y, then find the value of y.

A
20000

B
10000

C
15000

D
21000

Solution

Let the 1^st part = x
And 2^nd part = y = 30,000 - x
Interest for 1^st part =
Interest for 2^nd part =
=

20x = 40 Â´ 30000 - 40x
60x = 40 Â´ 30000
x = 20,000
hence y = 30,000 - 20,000
= Rs.10,000
Question 11
1 / -0

A machinery depreciates in cost every year at the rate of 5% of its value in the beginning of that year. Find out its original value if at the end of 3 years, its depreciated value is Rs. 205770

A
Rs. 238204

B
Rs. 250000

C
Rs. 240000

D
Rs. 177751

Solution

Let the value of machinery = x
Rate of depreciation = 5%
Time = 3 years
205770 =
=
x =
= Rs.240,000
Question 12
1 / -0

A certain sum of money at certain rate of interest amounts to Rs. 5900 in 3 years and Rs. 7400 in 8 years, it will amount to Rs. 8000 at the same rate of interest in

A
11 years

B
10 years

C
16 years

D
13 years

Solution

Amount in 3 years = Rs.5900
Amount in 8 years = Rs.7400
Hence interest for 5 years = 7400 - 5900 = 1500
Interest for 3 years =
= 900
Sum = 5900 - 900 = 5000
Rate = = 6%
Now amount = Rs.8000
Interest = 8000 - 5000
= 3000
Time = = 10 years
Question 13
1 / -0

Sahil borrows Rs. 16550 from Rishab to be paid back with compound interest at the rate of 10% p.a. in 3 years, in 3 equal yearly instalments. Find the value of each instalment.

A
Rs. 6500

B
Rs. 7000

C
Rs. 6600

D
Rs. 6655

Solution

Let the value of each equal instalment be Rs. e.
So, 16550(1 + 0.10)³ = e(1 + 0.10)²+ e(1 + 0.10) + e
Or, 16550(1.331) = 1.21e + 1.1e + e = 3.31e
Or, e = 6655
Thus, the equal instalment is of Rs. 6655.
Hence, answer option 4 is correct.
Question 14
1 / -0

A man borrows money at 6% per annum interest payable yearly and lends it immediately at 6% per annum compound interest payable half-yearly and thereby gains Rs. 45 at the end of the year. What is the sum borrowed?

A
Rs. 50,000

B
Rs. 40,500

C
Rs. 55,000

D
Rs. 60,000

Solution

Let the sum borrowed be Rs. x.
Rate = 6%
Time = 1 year
Amount = x =
He received interest payable half yearly.
= x
= x
x = 45
x = 45
= 45
x = = Rs. 50,000
Question 15
1 / -0

The compound interest on a certain sum for 3 years at the rate of 5% per annum is Rs. 2522. The simple interest on the same sum for double the time at half the rate percent per annum is:

A
Rs. 1600

B
Rs. 960

C
Rs. 2400

D
Rs. 800

Solution

Let sum = Rs. x
2522 =
2522 = x
2522 = x
x = 16,000
x = 16,000
R = %
T = 6 years
S.I. = = Rs. 2400
Question 16
1 / -0

There is 60% increase in an amount in 6 years at SI. What will be CI of Rs. 12000 after 3 years at the same rate?

A
Rs. 2160

B
Rs. 3600

C
Rs. 3972

D
Rs. 8736

Solution

Suppose, P = Rs. 100
Time = 6 years
Hence, interest = 160 - 100 = 60
Rate = = 10%
Now, P = Rs. 12000
T = 3 years
R = 10%
Amount = 12000
=
= Rs. 15972
Hence, CI = 15972 - 12000 = Rs. 3972
Question 17
1 / -0

A sum of money was borrowed and paid back in two annual equal installments of Rs. 882 each, paying 5% compound interest. The sum borrowed was

A
Rs. 1620

B
Rs. 1640

C
Rs. 1680

D
Rs. 1600

Solution

Let each instalment be Rs. x and principal for the first and the second years be P₁ and P₂, respectively.
x = P₁
P₁ =
x = P₂
P₂ =
P₁ + P₂ = x
P₁ + P₂ = x
P = 882 = 2 20 41 = Rs. 1640
Hence, the sum of money borrowed = Rs. 1640
Question 18
1 / -0

The least number of complete years in which a sum of money put at 25% C.I. will be more than treble is:

A
3

B
4

C
5

D
8

Solution

Let P = Rs.100
Rate = 25%
Time = 1 year
Interest = = 25
Amount after 1 year = 125
Interest for 2^nd year =
= 31.25
Amount after 2 years = 156.25
Amount after 3 years = 200.31
Amount after 4 years = 250.38
Amount after 5 years = 312.98
Hence after 5 years it will be treble
Question 19
1 / -0

The effective annual rate of interest corresponding to a nominal rate of 8% per annum payable quarterly is

A
8.24%

B
8.3%

C
8.2%

D
8.01%

Solution

Let P = Rs.100
R = 8%
T = 1 year (quarterly)
Amount = 100
=
= 108.24
Effective rate of interest = 108.24 - 100 = 8.24%
Question 20
1 / -0

A sum of money invested at compound interest amounts to Rs. 4624 in two years and Rs. 4913 in three years. The sum invested is

A
Rs. 4300

B
Rs. 4350

C
Rs. 4096

D
Rs. 4050

Solution

Amount in two years = Rs. 4624
Amount in three years = Rs. 4913
Hence, interest for one year on Rs. 4624 = Rs. 4913 - Rs. 4624 = Rs. 289

Rate = = 6.25%

Suppose the sum of money invested = Rs. P
Then, according to the question:
4624 =
4624 = P P = = Rs. 4096