Mathmetics

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

Q241.
If A: B  = 5 : 6  and  B : C = 4: 5 , then A: C  is equal to - 
1) 2:3 2) 4:5
3) 3:4 4) 6:7
5)None of these
Answer : 2:3
Explanation : Given, 
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Q242.
Salaries of A and B are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is B's salary ?
1) Rs.17,000 2) Rs.20,000
3) Rs.25,500 4) Rs.38,000
5)None of these
Answer : Rs.38,000
Explanation :
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Q243.
In a mixture of 60 liters, the ratio of milk and water 2 : 1. How many liters of water must  be added in to the mixture so that the ratio became 1 : 2 ?
1) 20 litres 2) 30 litres
3) 40 litres 4) 60 litres
5)None of these
Answer : 60 litres
Explanation :
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Q244.
Two numbers are respectively 20% and 50% more than a third number. What is the ratio of the two numbers ?
1) 2 : 5 2) 3 : 5
3) 4 : 5 4) 6 : 7
5)None of these
Answer : 4 : 5
Explanation :
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Q245.
What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?
1) 24 2) 38
3) 42 4) 48
5)Non of these
Answer : 38
Explanation :
Let, the numbers be x and x + 2.
Then, (x + 2)2 - x2 = 84
or 4x + 4 = 84    or  4x = 80
or x = 20. The required sum = x + (x + 2) = 2x + 2 = 42.
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Q246.
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. What is the number ?
1) 235 2) 253
3) 273 4) 352
5)None of these
Answer : 253
Explanation :
Let, the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.
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Q247.
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. What is the number ?
1) 18 2) 24
3) 42 4) 81
5)None of these
Answer : 24
Explanation :
Let, the ten's and unit digit be x and y respectively.
So, xy = 8 and the number be 10x+y
When 18 is added,  the number be 10x+ y +18.
Then, 10x + y + 18 = 10 y + x
or 9x - 9y = -18   x - y = - 2
 We know that (x+y)2=( x-y)2 + 4xy = (-2)2 + 4 x 8 =36
or x+y = 6
By solving we get x = 2 and  y = 4
Thus, the number is 24.
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Q248.
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by-
1) 3 2) 5
3) 10 4) 11
5)None of these
Answer : 11
Explanation :
Let, the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11
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Q249.
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2  ?
1) 4 2) 8
3) 12 4) 14
5)None of these
Answer : 8
Explanation :
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let, ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36   
or 9x = 36
or x = 4.
So, required difference = (2x + x) - (2x - x) = 2x = 8.
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Q250.
What will be remainder when (6767 + 67) is divided by 68 ?

1) 1 2) 53
3) 66 4) 67
5)None of these
Answer : 66
Explanation :
(xn + 1) will be divisible by (x + 1) only when n is odd.
(6767 + 1) will be divisible by (67 + 1)
(6767 + 1) + 66, when divided by 68 will give 66 as remainder.
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