Mathmetics

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

Q21.
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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Q22.
If (13+23+33+43+ 53+63+................+103) = 3025 ,then find the value of (23+43+63+83+ 103+...............+203) 
1) 6050 2) 10060
3) 12040 4) 24200
5)None of these
Answer : 24200
Explanation : We can express ,  (23+43+63+83+ 103+...............+203) = 
23 x  (13+23+33+43+ 53+63+................+103) = 8 x  3025 = 24200
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Q23.
Given that, (12+22+32+42+ 52+62+72) = x +1 , the find the value of the following expressions:

(22+42+62+82+102+122+ 142) =  ?
1) 2(x+1) 2) 4(x+1)
3) 8(x+2) 4) 16(x+1)
5)None of these
Answer : 4(x+1)
Explanation : We can write, (22+42+62+82+102+122+ 142) = 22 x (12+22+32+42+ 52+62+72 =  4(x+1)
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Q24.
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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Q25.
The sum of the present ages of A, B and C is 72 years. Also the sum of present ages of A and B is 42 years. What is the present age of C ?
1) 30 yrs 2) 24 yrs
3) 18 yrs 4) 36 yrs
5)None of these
Answer : 30 yrs
Explanation : The present age of C = 72 - 42 = 30 years
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Q26.
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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Q27.
A tank has three drain pipes, the first two pipes A and B operating simultaneously can empty the tank in half the time that of C, third pipe, alone takes to empty it. Pipe A working alone takes half the time taken by pipe B. Together they take to fill the tank in 6 hrs 40 mins. What is time taken for A to empty the tank alone ? 
1) 11hrs 2) 12 hrs
3) 11-1/9hrs 4) 12-1/3hrs
5)None of these
Answer : 11-1/9hrs
Explanation :

Let, C  pipe takes x hrs ,then A  pipe takes x/2 hrs

So, C  pipe takes  =2(x+x/2) =3x hrs

Then, (A+B+C) pipes can do in 1 hr = 1/x + 2/x +1/3x = 10/3x hrs

But given , total time taken by all pipes  = 6 hrs 40 min = 6-2/3 hrs = 20/3 hrs

So, 10/3x hrs = 3/20

Or x =200/9 hrs i.e time taken for pipe B

Therefore, time taken for pipe A = (200/9)/2 = 100/9 = 11-1/9hrs

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Q28.
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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Q29.
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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Q30.
The area of a rectangular field is 460 sq. mtrs. If the length is 15% more than the breadth, what is the breadth of the rectangular field ?
1) 15 mtrs 2) 26 mtrs
3) 25 mtrs 4) 20 mtrs
5)None of these
Answer : 20 mtrs
Explanation :
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