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

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Q81.	Two partners invested Rs.20,000 and Rs.12,000 respectively in a business.They distribute 75% of the profit equally and distribute the rest 25% according to the ratio of their investment of capitals. If the bigger partner received Rs.400 more than the other, then what is the total profit ?

1)	Rs.5280	2)	Rs.5600
3)	Rs.6240	4)	Rs.6400
5)	None of these

Answer : Rs.6400
Explanation : Since, 75% of the profit is distributed equally ,rest 25% should be distributed according to their ratio of investment.

Actual, ratio of capital = 20000:12000 = 5:3

5/8 - 3/8 = 400

or 2/8 = 1/4 = 400

or 1 = 4 x 400 = 1600 i.e. 25%

So, total profit = 400 x 4 x (1/25) x 100 = 6400

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Q82.	A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes ?

1)	1 : 6	2)	1 : 5
3)	1 : 25	4)	1 : 125
5)	None of these

Answer : 1 : 5
Explanation :

The volume of the larger cube = 53 = 125 cm³.

The volume of each of the smaller cubes = 13 = 1 cm³.

Therefore, one would get 125 smaller cubes.

The surface area of the larger cube = 6a² = 6(52) = 6 25 = 150

The surface area of each of the smaller cubes = 6 (12) = 6.

Therefore, surface area of all of the 125, 1 cm³ cubes = 125 6 = 750.

Therefore, the required ratio = 150 : 750 = 1 : 5

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Q83.

1)	8	2)	9
3)	10	4)	12
5)	None of these

Answer : 10
Explanation :

Given, x² + 9/x = 6x

Or x² - 6x = 9

Or (x-3)² = 0

Or x = 3

So, x² + 9/x²= 10

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Q84.	If a = 4/3, then, what is the value of 27a³ -108a²+ 144a - 317 ?

1)	221	2)	-231
3)	-253	4)	0
5)	None of these

Answer : -253
Explanation :

Given, a = 4/3

Or 3a = 4

Or 3a - 4 = 0

Or (3a-4)³ = 27a³ - 108a² + 144a - 64 = 0³

Or 27a³ - 108a² + 144a - 317 = (27a³ - 108a² + 144a -64) - 153 = 0 - 253 = - 253

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Q85.	A fort has provisions for 250 soldiers for 35 days. After 5 days a reinforcements of 25 soldiers were arrived. Again after 10 days, 25 soldiers left the fort. How long will the remaining provisions lasting ?

1)	12	2)	16
3)	18	4)	19
5)	None of these

Answer : 19
Explanation :

Short- Cut Methods:

ND (No. of days) = N₁D₁ + N₂D₂ = total amount of food after 5 days.

or ( 250 X 30) = ( 250 + 25) X 10 + 250 X x

or x = 19 days .

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Q86.	The ratio of the present age of A to that of B is 3 : 11. B is 12 years younger than C. C ''s age after 7 years will be 85 years. What is the present age of A's father, who is 25 years older than A ?

1)	33 years	2)	40 years
3)	43 years	4)	48 years
5)	None of these

Answer : 43 years
Explanation :

Present age of C = 85 � 7 = 78 years

Present age of B = 78 � 12 = 66 years

Present age of A = 3

11 66 = 18 years

Present age of A�s father = 18 + 25 = 43 years

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Q87.	The length of a rectangle is three-fifths of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle if the breadth of the rectangle is 8 cm ?

1)	100.8 sq cm	2)	112.4 sq cm
3)	104.2 sq cm	4)	Cannot be determined
5)	None of these

Answer : 100.8 sq cm

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Q88.	The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?

1)	136�	2)	156�
3)	168�	4)	208�
5)	None of these

Answer : 168�
Explanation :

Sum of the adjacent angles of a parallelogram is 180�.

Smaller angle of the parallelogram = 7/15 � 180 = 84�

Second largest angle of the quadrilateral = 7/30 � 360 = 84�

Required sum = 84 + 84 = 168�

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Q89.	The smallest side of a right-angled triangle is 8 cm less than the side of a square of perimeter 56 cm. The second largest side of the right-angled triangle is 4 cm less than the length of the rectangle of area 96 sq cm and breadth 8 cm. What is the largest side of the right-angled triangle ?

1)	10 cm	2)	12 cm
3)	15 cm	4)	18 cm
5)	None of these

Answer : 10 cm
Explanation :

Side of the square = 56/4 = 14 cm

smallest side of the triangle = 14 � 8 = 6 cm

Length of the rectangle = 96/ 8 = 12 cm

Second largest side of the triangle = 112 � 4 = 8 cm

So, Largest side of the triangle = square root of 6² + 8² = 10 cm

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Q90.	A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed?

1)	26	2)	27
3)	41	4)	56
5)	None of these

Answer : 41

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Mathmetics

Q81.

Two partners invested Rs.20,000 and Rs.12,000 respectively in a business.They distribute 75% of the profit equally and distribute the rest 25% according to the ratio of their investment of capitals. If the bigger partner received Rs.400 more than the other, then what is the total profit ?

Q82.

A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes ?

Q83.

Q84.

If a = 4/3, then, what is the value of 27a3 -108a2 + 144a - 317 ?

Q85.

A fort has provisions for 250 soldiers for 35 days. After 5 days a reinforcements of 25 soldiers were arrived. Again after 10 days, 25 soldiers left the fort. How long will the remaining provisions lasting ?

Q86.

The ratio of the present age of A to that of B is 3 : 11. B is 12 years younger than C. C ''s age after 7 years will be 85 years. What is the present age of A's father, who is 25 years older than A ?

Q87.

The length of a rectangle is three-fifths of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle if the breadth of the rectangle is 8 cm ?

Q88.

The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?

Q89.

The smallest side of a right-angled triangle is 8 cm less than the side of a square of perimeter 56 cm. The second largest side of the right-angled triangle is 4 cm less than the length of the rectangle of area 96 sq cm and breadth 8 cm. What is the largest side of the right-angled triangle ?

Q90.

A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed?

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If a = 4/3, then, what is the value of 27a³ -108a²+ 144a - 317 ?