Mathmetics

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

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Q1.
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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Q2.
The length of a rectangle increases by 20% and also  its breadth increases by 15% . What should be the percentage change in its perimeter?
1) 35% 2) 36%
3) 38% 4) Can't be determined
5)None of these
Answer : Can't be determined
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Q3.
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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Q4.
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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Q5.
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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Q6.
The length of a rectangle is increased to 3/2 times of its length and breadth is reduced to 1/3rd of its breadth. What is the change in area ?
1) 1/3 2) 1/4
3) 1/2 4) No change
5)None of these
Answer : 1/2
Explanation :
Let the length and breadth of the rectangle be L and B respectively.
Area = L x B = LB


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Q7.
The ratio of angle of a triangle is 3 : 5 : 7. What is the difference between double the smallest angle and half of the largest angle (degree) ?
1) 25 2) 36
3) 38 4) 30
5)None of these
Answer : 36
Explanation :
The smallest angle = 3/15 x 180° = 36°
The largest angle =7/15 x 180° = 84°
So, (36 x 2) - (84/ 2) = 36 
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Q8.
What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm ?
1) 344.35 cm2 2) 462 cm2
3) 498.35 cm2 4) 456cm2
5)None of these
Answer : 498.35 cm2
Explanation :
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Q9.
The sides of a triangle are in the ratio 1/3:1/4:1/5 and its perimeter is 94cm. What is the length of the smallest side of the triangle ?
1) 18.8 cm 2) 23.5 cm
3) 24 cm 4) 31.3cm
5)None of these
Answer : 24 cm
Explanation :
The final ratio of the triangle are 20 : 15 : 12
Perimeter = 20x + 15x + 12x = 47 x 
So, 47x = 94 
or = x = 2
Thus smallest side = 122 = 24 cm.
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Q10.
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle ?
1) 16 cm 2) 18 cm
3) 24 cm 4) Data Inadequate
5)None of these
Answer : 18 cm
Explanation :
2(l + b) /b = 5/1 or 2l + 2b = 5b
or  3b = 2l   b =2l/3 
Then, Area = 216 cm2
l x b = 216
l x2l/3  = 216 or l= 324
or l = 18 cm.
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