Mathmetics

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

Q61.
There are  5 men and 3 women to form a committee of 5-members where at least 3 men are there. How many way they can be selected ?
1) 42 2) 45
3) 46 4) 54
5)None of these
Answer : 46
Explanation :  Total ,5 men and 3 women i.e. 8 persons.
So, 3 men can selected from 5 men.
They can selected in (5C3  x 3 C2 ) or (5C4  x 3 C1 ) or (5C5  x 3 C0
Total numbers of way to select = [(5 x 4 )/2 x 3 ] +[(5 ) x 3 ] + [(1x 1) ] = 46

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Q62.
The sum of two numbers is 27 and their H.C.F is 3. If one of the number is lies between  13 to 16, the find the value of the other number ?
1) 12 2) 15
3) 18 4) 24
5)None of these
Answer : 12
Explanation : Let, two numbers are 3x and 3y respectively.
Then, 3x + 3y = 27  
 or 3 (x + y) = 27
or (x + y) = 27/3 = 9
So, pairs of numbers are  9 = (1,8) , (2,7) , ( 3,6) and  (4,5) .
Thus the numbers are 3 x 4 = 12 and 3 x 5 =15 
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Q63.
 A , B and C invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. A left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of B ?
1) Rs.820 2) Rs.890
3) Rs.1020 4) Rs.1250
5)None of these
Answer : Rs.890
Explanation :
A : B : C = (8,000 x 6) : (4,000 x 8) : (8,000 x 8) = 48 : 32 : 64 = 3 : 2 : 4.
B's share = ( Rs. 4005/9) x 2 = Rs. 890.
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Q64.
 A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, what is the total profit ?
1) Rs.1200 2) Rs.1250
3) Rs.1450 4) Rs.1500
5)None of these
Answer : Rs.1500
Explanation :
Let, the total profit be Rs. 100.
After paying to charity, A's share = (Rs. 95 /5)x 3 = Rs. 57.
If A's share is Rs. 57, total profit = Rs. 100.
If A's share Rs. 855, total profit = ( 855/57) x100  = 1500

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Q65.
The ratio between the profit and the sale price of an article is 1 : 5. What is the ratio between the sale and the cost price of that article ?
1) 4 : 5 2) 5 : 4
3) 3 : 2 4) Data Inadequate
5)None of these
Answer : 5 : 4
Explanation :
C.P. = S.P. - Profit 
or C.P. = 5 -1 = 4
or S.P. : C.P. = 5 : 4
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Q66.
A sum was put at a certain rate of interest for 5 years. Had it been put at 2% higher rate, it would have fetched Rs. 72 more. What is the sum ?
1) Rs. 4,250 2) Rs. 4,500
3) Rs. 6,400 4) Rs. 7200
5)None of these
Answer : Rs. 7200
Explanation :
We know that Sum = (S.I X 100 )/ R X T
 = (Diff. in S.I X 100 ) / Diff. in rate X Time 
= (72 X100)/ 2 X 5 =  Rs. 7200.
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Q67.
In what proportion should a milkman mix milk at Rs.2.40 per litre and Rs.3.60 per litre to make a mixture worth Rs.2.50 per litre ?
1) 5: 17 2) 1:11
3) 11:1 4) 2:3
5)None of these
Answer : 11:1
Explanation :
By alligation method :-
2.40 3.60

2.50

3.60 - 2.50 2.50 - 2.40
= 1.10 10
So, Ratio will be 11 : 1.

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Q68.
A river is flowing at 2 kmph. It takes a man twice as long to row up as, to row down the river. What is the rate (in km/hr) of the man in still water ?
1) 2 2) 4
3) 6 4) 8
5)None of these
Answer : 6
Explanation :
Let,speed of boat man be x kmph.
So, speed in down stream =(x+2) kmph. and speed in up-stream = (x-2) kmph.
Since, distance is constant for both case ,
the equation = 2(x-2) = (x+2)
or 2x-4 = x+2
or x= 6 kmph

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Q69.
The speed of a car increases by 2 km after every hour. If the distance travelled in the first hour was 35 km. What was the total distance travelled in 12 hours ?
1) 456 km 2) 482 km
3) 548 km 4) 552 km
5)None of these
Answer : 552 km
Explanation :
Given, the first term,  a = 35, common difference, d = 2 and total number of terms,  (n) = 12. 
The sum of this series will be the total distance travelled.
Sum,  Sn= n/2[2a + (n - 1) d] = 6 [70 + 11 x 2] = 552 km.

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Q70.
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) 9 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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