Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

Area Average Bankers Discount Boats and Streams Calendar Chain Rule Clock Compound Interest Decimal Fraction Height and Distance Logarithm Mixture Numbers Odd Man Out and Series Partnership Percentage Permutation and Combination Pipes and Cistern Probability Problems on Ages Problems on H.C.F and L.C.M Problems on Numbers Problems on Trains Profit and Loss Races and Games Ratio and Proportion Simple Interest Simplification Square Root and Cube Root Stocks and Shares Surds and Indices Time and Distance Time and Work True Discount Volume and Surface Area

Q. If log4(64) = x, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

64 = 4^3, so x = 3.

Correct Answer: B — 3

Q. If log7(343) = x, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

343 = 7^3, so x = 3.

Correct Answer: A — 3

Q. If log7(49) = x, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

49 = 7^2, so x = 2.

Correct Answer: B — 2

Q. If log7(x) = 2, what is the value of x?

A. 14
B. 28
C. 49
D. 56

Solution

x = 7^2 = 49.

Correct Answer: C — 49

Q. If log7(x) = 3, what is the value of x?

A. 49
B. 21
C. 7
D. 14

Solution

x = 7^3 = 343.

Correct Answer: A — 49

Q. If logb(64) = 6, what is the value of b?

A. 2
B. 4
C. 8
D. 16

Solution

64 = b^6, so b = 64^(1/6) = 2.

Correct Answer: C — 8

Q. If logx(100) = 2, what is the value of x?

A. 10
B. 20
C. 30
D. 40

Solution

x^2 = 100, so x = 10.

Correct Answer: A — 10

Q. If logx(27) = 3, what is the value of x?

A. 3
B. 9
C. 27
D. 81

Solution

x = 27^(1/3) = 3.

Correct Answer: C — 27

Q. If logx(49) = 2, what is the value of x?

A. 5
B. 7
C. 14
D. 49

Solution

x^2 = 49, so x = 7.

Correct Answer: B — 7

Q. If logx(64) = 6, what is the value of x?

A. 2
B. 4
C. 8
D. 16

Solution

x = 64^(1/6) = 2.

Correct Answer: C — 8

Q. If logx(81) = 4, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

x = 81^(1/4) = 3.

Correct Answer: A — 3

Q. If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how long will it take to fill the tank if both pipes are opened together?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.

Correct Answer: B — 5 hours

Q. If the age of a woman is 3 times the age of her daughter and the sum of their ages is 48, what is the age of the daughter?

A. 8
B. 12
C. 16
D. 20

Solution

Let the daughter's age be x. Then the woman's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. If the age of a woman is 3 times the age of her daughter and the sum of their ages is 48, how old is the daughter?

A. 8
B. 12
C. 16
D. 20

Solution

Let the daughter's age be x. Then the woman's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. If the average of 10 numbers is 50 and the average of another 10 numbers is 60, what is the average of all 20 numbers?

A. 55
B. 56
C. 57
D. 58

Solution

Total of first 10 numbers = 10 * 50 = 500. Total of second 10 numbers = 10 * 60 = 600. Combined total = 500 + 600 = 1100. Average = 1100 / 20 = 55.

Correct Answer: A — 55

Q. If the average of 4 numbers is 15, what is the sum of those numbers?

A. 45
B. 60
C. 75
D. 90

Solution

The sum of the numbers is 4 * 15 = 60.

Correct Answer: A — 45

Q. If the average of 6 numbers is 12 and the average of 4 other numbers is 15, what is the average of all 10 numbers?

A. 13
B. 14
C. 15
D. 16

Solution

Total of first 6 numbers = 6 * 12 = 72. Total of next 4 numbers = 4 * 15 = 60. Combined total = 72 + 60 = 132. Average = 132 / 10 = 13.2.

Correct Answer: B — 14

Q. If the average of 8 numbers is 50, what is the average if one number is removed and it was 60?

A. 48
B. 49
C. 50
D. 51

Solution

Total = 50 * 8 = 400. New total = 400 - 60 = 340. New average = 340 / 7 = 48.57.

Correct Answer: B — 49

Q. If the average of 8 numbers is 50, what is the average if one number is removed and the new average is 52?

A. 50
B. 51
C. 52
D. 53

Solution

Total of 8 numbers = 50 * 8 = 400. New total = 52 * 7 = 364. The removed number = 400 - 364 = 36.

Correct Answer: B — 51

Q. If the average of five numbers is 12, what is their total sum?

A. 48
B. 60
C. 72
D. 84

Solution

Total sum = Average * Number of items = 12 * 5 = 60.

Correct Answer: A — 48

Q. If the average of three numbers is 15 and the first two numbers are 10 and 20, what is the third number?

A. 10
B. 15
C. 20
D. 25

Solution

Total of three numbers = 3 * 15 = 45. Sum of first two numbers = 10 + 20 = 30. Third number = 45 - 30 = 15.

Correct Answer: D — 25

Q. If the Banker's Discount on a bill of $800 is $16, what is the rate of interest for 4 months?

A. 5%
B. 6%
C. 7%
D. 8%

Solution

Rate = (BD x 100) / (Principal x Time) = (16 x 100) / (800 x 4/12) = 6%

Correct Answer: B — 6%

Q. If the Banker's Discount on a bill of Rs. 20000 due in 6 months at 10% is Rs. 1000, what is the true discount?

A. Rs. 800
B. Rs. 1000
C. Rs. 1200
D. Rs. 600

Solution

True Discount = Banker's Discount × (Time / (Time + 1)) = 1000 × (0.5 / (0.5 + 1)) = Rs. 666.67.

Correct Answer: A — Rs. 800

Q. If the Banker's Discount on a bill of Rs. 22000 due in 5 months at 6% is Rs. 550, what is the true discount?

A. Rs. 500
B. Rs. 550
C. Rs. 600
D. Rs. 450

Solution

True Discount = Banker's Discount × (Time / (Time + 1)) = 550 × (5/12) = Rs. 229.17.

Correct Answer: A — Rs. 500

Q. If the Banker's Discount on a bill of Rs. 8000 due in 1 year at 12% is Rs. 960, what is the true discount?

A. Rs. 800
B. Rs. 960
C. Rs. 720
D. Rs. 640

Solution

True Discount = Banker's Discount × (Time / (Time + 1)) = 960 × (1 / (1 + 1)) = Rs. 480.

Correct Answer: C — Rs. 720

Q. If the Banker's Discount on a bill of Rs. 8000 due in 6 months at 12% per annum is Rs. 480, what is the true discount?

A. Rs. 400
B. Rs. 480
C. Rs. 600
D. Rs. 500

Solution

True Discount = Banker's Discount * (Time / (Time + 1)) = 480 * (6/12) = Rs. 240.

Correct Answer: A — Rs. 400

Q. If the Banker's Discount on a loan of $3000 is $90 for 3 months, what is the rate of interest?

A. 6%
B. 7%
C. 8%
D. 9%

Solution

Rate = (BD x 100) / (Principal x Time) = (90 x 100) / (3000 x 3/12) = 12%

Correct Answer: A — 6%

Q. If the bankers discount on a sum of $8000 for 1 year at 12% is $960, what is the present value?

A. $7040
B. $7048
C. $7200
D. $7208

Solution

Present Value = Principal - Bankers Discount = 8000 - 960 = $7040.

Correct Answer: A — $7040

Q. If the bankers' discount on a bill is Rs. 400 and the time is 1 year at a rate of 8% per annum, what is the face value of the bill?

A. Rs. 5000
B. Rs. 6000
C. Rs. 7000
D. Rs. 8000

Solution

Face Value = BD / (Rate × Time) = 400 / (0.08 × 1) = Rs. 5000.

Correct Answer: B — Rs. 6000

Q. If the bankers' discount on a bill is Rs. 400 and the time is 4 months, what is the face value of the bill at the rate of 12% per annum?

A. Rs. 4000
B. Rs. 5000
C. Rs. 6000
D. Rs. 7000

Solution

Face Value = BD / (Rate × Time) = 400 / (12 × 4/12) = Rs. 5000.

Correct Answer: B — Rs. 5000

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