Mathmetics

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

Q61.
 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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Q62.
 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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Q63.
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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Q64.
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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Q65.
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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Q66.
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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Q67.
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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Q68.
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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Q69.
The cost of 16 pens and 12 pencils is Rs. 720. What is the cost of 20 pens and 15 pencils ?
1) Rs.800 2) Rs.840
3) Rs. 880 4) Rs.900
5)None of these
Answer : Rs.900
Explanation :
Let, the price of the pen be ‘x’ and that of a pencil be ‘y’.
16x + 12y = 720 or (16x) X 5/4 + 12y X 5/4 = 720 X 5/4 
or 20x + 15y = 900
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Q70.
The ratio of the sum and the difference of two numbers is 3: 1. Then what is the ratio of these two numbers ?
1) 3 : 2 2) 2 : 1
3) 3 : 1 4) 4 : 3
5)None of these
Answer : 2 : 1
Explanation :
Let, the number be ‘x’ and ‘y’
So, (x+y)/(x-y) = 3/1
or x + y = 3x - 3y  
or 2x = 4y
or x:y = 2:1 
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