Quantitative aptitude Question for all banking Bank PO,Clerk,IBPS PO,Railway,SSC,PSUs,IAS,OAS ,C-SAT Exams

Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

Q21.	An article is marked x% above the cost price. A discount of 2x/3% is given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then what should be the value of 50% of x ?

1)	12	2)	14
3)	15	4)	20
5)	None of these

Answer : 15
Explanation :

Let, the cost price of the article is Rs.100. Marked price (MP) = Rs.100+x

Selling price of the price (SP) = MP - discount = Rs.100+x - 2x/3 *(Rs.100+x)/100

Also, SP = CP + 4% profit = 100+4 = Rs.104

Hence,(100+x)-2/3x * (100+x)/100 = 104

or 100+x - 2x/300 (100+x) = 104

or x² - 50x + 600 = 0

On solving the above equation, we get possible values of x as 20 and 30. But as x lies between 25 and 50, the value should be 30.

So, x = 30.

The value of 50% of x is = 15

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Q22.	How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed ?

1)	30	2)	48
3)	60	4)	120
5)	None of these

Answer : 60
Explanation :

Let the 3-digit number be ABC, where C is at the units place, B at the tens place and A at the hundreds place.

Now when repetition is not allowed,

The number of digits possible at C is 5. Let’s suppose one of 5 digits occupies place C, now as the repletion is not allowed, the possible digits for place B are 4 and similarly there are only 3 possible digits for place A.

Therefore, The total number of possible 3-digit numbers = 5 × 4 × 3=60

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Q23.	How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed ?

1)	60	2)	90
3)	120	4)	240
5)	None of these

Answer : 120
Explanation : Let the 3-digit number be ABC, where C is at the units place, B at the tens place and A at the hundreds place.
Now when repetition is allowed,
The number of digits possible at C is 5. As repetition is allowed, the number of digits possible at B and A is also 5 at each.
Hence, the total number possible 3-digit numbers =5 × 5 × 5 =125

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Q24.

Two patterners A and B invested Rs. 1250/ and Rs.850 in a in a business respectively. Both the patterners distributes 37% of the profits equally and rest of the profit according to their ratio of capital investments. If one partners gets Rs.30 more than other, then what should be the total profit in the business.

1)	Rs.225	2)	Rs.250
3)	Rs.275	4)	Rs.280
5)	None of these

Answer : Rs.250
Explanation : The ratio of capital of A and B =1250:850 = 25:17

A and B equally share the total of 37%.

Now, rest 63% is divided in the ratio 25:17.

So, A.T.Q (63/42) x 25 - (63/42)x 17 = Rs.30

Or (63/42) x (25-17) = (63/42) x 8 = 30

Or (1.5 x 8 ) % = 30

So, total profit =i.e. 100% =12 x 30 =Rs.250

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Q25.	The LCM and HCF of two numbers are 660 and 10 respectively. If the sum of the numbers is 170, the what should be difference of the numbers ?

1)	30	2)	40
3)	48	4)	50
5)	None of these

Answer : 50
Explanation : Let , two numbers are 10a and 10b ,where a and b are relatively prime numbers.

According to the question,10a X b = 660

or ab = 66 ------------- (i)

Also given, 10a + 10b = 170

or a + b = 17 ------------------- (ii)

Solving Eqs. (i) and (ii) we get a = 11 and b = 6

So, numbers are 110 and 60.

Thus, the difference is 110 - 60 = 50

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Q26.	Thrice the age of A is 7 times B's age. And C’s age is half of A's age. Also, nine years ago, A's age was one-third of B’s age then. What is the ratio between the age of the A,B and C age respectively ?

1)	11:6:7	2)	11:6:3
3)	14:6:3	4)	14:6:7
5)	None of these

Answer : 14:6:7
Explanation : Given, 3A = 7B

or 3A - 7B = 0 ---------(I) and A = 2C --------- (II)

And A-9 = (B-9)/3

or 3A-27 = B-9

or 3A - B = 18 ---------- (III)

from equations I and III , we get B = 3

A= 7 and C = 3.5

So, ratio of A,B and C i.e. A:B:C= 14:6:7

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Q27.	The perimeter of a square field is 16 m more than the perimeter of a rectangle. The length of the rectangle is 40m which is 250% of its width. If a street of width 4 m surrounds from outside the square, then find the total cost of constructing the street at the rate of Rs. 20 per sq. m?

1)	Rs.10,480	2)	Rs.11,240
3)	Rs.11,520	4)	Rs.12,420
5)	None of these

Answer : Rs.11,520
Explanation :

Let the width of the rectangle = x m

Then, 250% of x = 40

x = 40 × 100/250 = 16 m

Perimeter of the rectangle = 2(length + width) = 2 × (40 + 16) = 112 cm

Perimeter of the square = (112 + 16) = 128 m

The sides of the square = 128/4 = 32 m

The area of the square field without street = (32)² sq. cm = 1024 sq. m

The area of the square field with street = (32 + 8)² sq. cm = 1600 sq. m

The area of the street = 1600 - 1024 = 576 sq. m

The total cost of constructing the street = 576 × 20 = Rs.11,520

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Q28.

A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2 : 1, earning annual interest at the rates of 4% and 3%, respectively. If the total annual interest income is Rs 76000 then what was the amount (in Rs lakh) invested in the fixed deposit ?

1)	Rs. 6 Lakhs	2)	Rs. 7 Lakhs
3)	Rs. 8 Lakhs	4)	Rs. 9 Lakhs
5)	None of these

Answer : Rs. 9 Lakhs
Explanation :

Let Rs x be invested in FD.

So, Remaining amount = Rs. 15 Lakhs - x, which is invested in the ratio 2 : 1

So, each investment would have 1/3(15-x) and 2/3(15-x) investments respectively

So, Total annual interest income = 6% of x + 4% of 1/3(15-x) + 3% of 2/3(15-x) = 76000

Rewriting Rs.76000 as Rs. 0.76 Lakhs,

6% of x + 4% of 1/3(15-x) + 3% of 2/3(15-x) = 0.76

Multiply both sides by 100,

6x + 4/3(15-x) + 2(15-x) = 76

6x +11/3 (15-x) = 76

165 + 18x -11x = 228

7x = 63

x = 9 (or) Rs. 9 Lakhs

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Q29.	A student scores 50% in an examination and after review, even though his score is increased by 40%, he fails by 30 marks. If his post-review score is increased by 20%, he will have 12 marks more than the passing score. What should be the percentage of mark needed for passing the examination ?

1)	60	2)	70
3)	72	4)	80
5)	None of these

Answer : 80
Explanation :

Let, the total Maximum marks in exam = 100%

His score = 50% of 100 = 50

His marks after review = 140% of 50 = 70

His marks after post review = 120% of 70 = 84

A.T.Q 84% – 12 =70% + 30

14% = 42

or 100% = 300

So passing marks = 300(70/100) + 30 = 240

Total marks = 100% = 300

Thus, required percentage score needed for passing the examination = (240/300 ) X 100 = 80%

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Q30.

A can complete a workpiece in 12 days. B requires 18 days to finish the same workpiece, whereas C can do it in 24 days. All three of them started working on the same workpiece, but due to some reason, C left work after working for 3 days with A and B. What should be the overall time taken to complete this workpiece ?

1)	5-3/10 days	2)	6-7/10 days
3)	6-3/10 days	4)	7-3/10 days
5)	None of these

Answer : 6-3/10 days
Explanation : A,B and C altogether work for 3 days = 3 (1/12+1/18+1/24) = 13/24 parts

So, remaining (1-13/24) = 11/24 parts

B and C can do in 1 day (1/12+1/18) = 5/36 parts

Now, B & C can do this in (11/24 )/(5/36) = 33/10 days = 3-3/10 days

So, overall time taken to complete this workpiece = 6-3/10 days

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Mathmetics

Q21.

An article is marked x% above the cost price. A discount of 2x/3% is given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then what should be the value of 50% of x ?

Q22.

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed ?

Q23.

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed ?

Q24.

Q25.

The LCM and HCF of two numbers are 660 and 10 respectively. If the sum of the numbers is 170, the what should be difference of the numbers ?

Q26.

Thrice the age of A is 7 times B's age. And C’s age is half of A's age. Also, nine years ago, A's age was one-third of B’s age then. What is the ratio between the age of the A,B and C age respectively ?

Q27.

The perimeter of a square field is 16 m more than the perimeter of a rectangle. The length of the rectangle is 40m which is 250% of its width. If a street of width 4 m surrounds from outside the square, then find the total cost of constructing the street at the rate of Rs. 20 per sq. m?

Q28.

Q29.

A student scores 50% in an examination and after review, even though his score is increased by 40%, he fails by 30 marks. If his post-review score is increased by 20%, he will have 12 marks more than the passing score. What should be the percentage of mark needed for passing the examination ?

Q30.

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