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Question 1 of 5
1. Question
The length of a rectangle is decreased by 20% and breadth increased by 20%. What will be the net percentage increase/decrease in the area of the rectangle?
Correct
Solution: D
Let the original length of the rectangle is x units
Let the original length of the rectangle be y units.
Thus, original area of rectangle = xy units^2 .
If the length of a rectangle is decreased by 20%, then new length will be 0.8 x units.
If breadth of rectangle is increased by 20%, then new breadth will be 1.2 y units.
Area of new rectangle will be 0.8x * 1.2y units^2
- Area of new rectangle will be = 0.96 xy units^2
Hence, Area of new rectangle will be 4 % less than the area of original rectangle.
Hence, option (d) is correct.
Incorrect
Solution: D
Let the original length of the rectangle is x units
Let the original length of the rectangle be y units.
Thus, original area of rectangle = xy units^2 .
If the length of a rectangle is decreased by 20%, then new length will be 0.8 x units.
If breadth of rectangle is increased by 20%, then new breadth will be 1.2 y units.
Area of new rectangle will be 0.8x * 1.2y units^2
- Area of new rectangle will be = 0.96 xy units^2
Hence, Area of new rectangle will be 4 % less than the area of original rectangle.
Hence, option (d) is correct.
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Question 2 of 5
2. Question
A man buys an article for 20% less than its value and sells it for 20 % more than its value. What is his gain in percentage?
Correct
Solution: A
Unconventional Method:
Let’s assume actual value of article is Rs. 100.
Therefore, buying price is 100-20 = Rs. 80 (As man bought with 20% less than actual value).
Selling price of article is 100 + 20 = Rs. 120 (As man sold with 20% more than actual value).
Therefore, gain in percentage = [(120-80)/80] * 100
è (40/80) * 100 = 50 %
Hence, option (a) is correct
Formula Method:
Let the original price of the article be ‘x’.
Buying price will be (80/100)x = 0.8x.
Selling price will be (120/100)x = 1.2x
Therefore, gain in percentage =(profit/buying price) * 100
- [(1.2x-0.8x)/0.8 x]* 100
- 5x * 100 = 50 %
Hence, option (a) is correct.
Incorrect
Solution: A
Unconventional Method:
Let’s assume actual value of article is Rs. 100.
Therefore, buying price is 100-20 = Rs. 80 (As man bought with 20% less than actual value).
Selling price of article is 100 + 20 = Rs. 120 (As man sold with 20% more than actual value).
Therefore, gain in percentage = [(120-80)/80] * 100
è (40/80) * 100 = 50 %
Hence, option (a) is correct
Formula Method:
Let the original price of the article be ‘x’.
Buying price will be (80/100)x = 0.8x.
Selling price will be (120/100)x = 1.2x
Therefore, gain in percentage =(profit/buying price) * 100
- [(1.2x-0.8x)/0.8 x]* 100
- 5x * 100 = 50 %
Hence, option (a) is correct.
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Question 3 of 5
3. Question
Two trains of lengths 150 m and 180 m respectively are running in opposite directions on parallel tracks. If their speed is 50 km/hour and 58 km/hour respectively. In how much time will they cross each other?
Correct
Solution: A
Standard Formula:
Suppose A and B are two objects with lengths L1 and L2 respectively, and their speeds are S1 and S2 respectively and moving in opposite direction, then
Crossing Time (Ct)= (Length of the objects)/(Relative speed of the objects)
Thus, Ct= (L1+L2)/(S1 +S2)
By looking at the above problem, we can say that,
L1= 150 m,
L2= 180 m,
S1= 50 km/hr
S2= 58 km/hr
Relative speed= (S1+S2)= 108 km/hr or (108 * 5/18) m/s = 30 m/s.
Therefore, crossing time Ct= (L1+L2)/ Relative speed
- Ct= (150 m+180 m)/ 30 m/s
- Ct= 330 m / 30 m/s = 11 seconds
Hence, option (a) is correct.
Incorrect
Solution: A
Standard Formula:
Suppose A and B are two objects with lengths L1 and L2 respectively, and their speeds are S1 and S2 respectively and moving in opposite direction, then
Crossing Time (Ct)= (Length of the objects)/(Relative speed of the objects)
Thus, Ct= (L1+L2)/(S1 +S2)
By looking at the above problem, we can say that,
L1= 150 m,
L2= 180 m,
S1= 50 km/hr
S2= 58 km/hr
Relative speed= (S1+S2)= 108 km/hr or (108 * 5/18) m/s = 30 m/s.
Therefore, crossing time Ct= (L1+L2)/ Relative speed
- Ct= (150 m+180 m)/ 30 m/s
- Ct= 330 m / 30 m/s = 11 seconds
Hence, option (a) is correct.
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Question 4 of 5
4. Question
Somebody has asked Amit about his age he said “My age is neither a perfect square nor a perfect cube”. He also said “My age is less than 60 years and more than 70 years”. What is Amit’s age if it is known that Amit always lies?
Correct
Solution: A
Since, it is known that Amit always lies, we should reverse his statements.
Therefore, his age is both perfect square as well as perfect cube as he said “My age is neither a perfect square nor a perfect cube”.
Also, his age is more than 60 years and less than 70 years as he said My age is less than 60 years and more than 70 years”
Thus, we have to find out for a number between 60 and 70 which is both perfect square as well as perfect cube. Hence 64 (i.e 8^2 and 4^3) is the required number.
Hence, option (a) is correct.
Incorrect
Solution: A
Since, it is known that Amit always lies, we should reverse his statements.
Therefore, his age is both perfect square as well as perfect cube as he said “My age is neither a perfect square nor a perfect cube”.
Also, his age is more than 60 years and less than 70 years as he said My age is less than 60 years and more than 70 years”
Thus, we have to find out for a number between 60 and 70 which is both perfect square as well as perfect cube. Hence 64 (i.e 8^2 and 4^3) is the required number.
Hence, option (a) is correct.
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Question 5 of 5
5. Question
Directions for the following 3 (three) items
Study the given information carefully and answer the question that follows:
There are six members A, B, C, D, E and F in a family having different professions such as Doctor, interior decorator, teacher, engineer, doctor and lawyer but not necessarily in respective order. There are two married couples in the family. D is a doctor and his wife is an interior decorator. A is the granddaughter of F and sister of C, who is a teacher. B is the grandfather of C and is married to a professor. A’s mother is an interior decorator and is the daughter-in-law of an engineer.
What is the profession of A?
Correct
Solution: C
From the above given information, we can have following observations:
D is doctor and married. D’s wife is interior designer.
A is sister of C who is a teacher.
A is granddaughter of F.
A’s mother is interior designer.
A’s mother is daughter in law of Engineer, thus A is granddaughter of Engineer.
B is grandfather of C. Since, A is sister of C, thus B is grandfather of A as well.
Since, both B and F are grandparents to A and C, B and F are married couple.
Since, B is married to professor, F’s profession is professor.
Since, A is granddaughter of Engineer, B’s profession is Engineer.
Remaining person is E, who is mother of A and is interior designer by profession. D and E are married couple.
Remaining, profession is Lawyer. Therefore, A’s profession is lawyer.
Hence, option (c) is correct.
Incorrect
Solution: C
From the above given information, we can have following observations:
D is doctor and married. D’s wife is interior designer.
A is sister of C who is a teacher.
A is granddaughter of F.
A’s mother is interior designer.
A’s mother is daughter in law of Engineer, thus A is granddaughter of Engineer.
B is grandfather of C. Since, A is sister of C, thus B is grandfather of A as well.
Since, both B and F are grandparents to A and C, B and F are married couple.
Since, B is married to professor, F’s profession is professor.
Since, A is granddaughter of Engineer, B’s profession is Engineer.
Remaining person is E, who is mother of A and is interior designer by profession. D and E are married couple.
Remaining, profession is Lawyer. Therefore, A’s profession is lawyer.
Hence, option (c) is correct.
