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Numerical Ability for SBI Clerk 26th Feb 2018

image 2018-02-26 15:09:44
Numerical Ability for SBI Clerk 26th Feb 2018

1. If a shopkeeper sales a cow at 16(2/3) % profit and a buffalo at 12(1/2)% loss, he gains Rs. 30 in whole transaction. If he sales a cow at 12.5 % loss and the buffalo at 16(2/3)% profit he neither gains nor losses. Find sum of their prices ?
(a)    620
(b)   720
(c)    725
(d)   625
(e)   None of these

2. When a train is running at a speed of 7/11 of its usual speed, it takes 22 hours to cover a certain distance. Find the actual time to cover the certain distance ?
(a)    14 hours
(b)   20 hours
(c)    8 hours
(d)   12 hours
(e)   None of these

3. Three taps A, B and C can file a tank in 12 hours, 15 hours and 20 hours respectively. First tap opened at 7 am., 2nd tap opened at 10 am. and 3rd tap opened at 11 am. At what time the tank will fill completely ?
(a)    3PM
(b)   2PM
(c)    6PM
(d)   1PM
(e)   None of these

4. Two trains running in opposite directions cross a man standing on platform in 28 sec and 15 sec respectively, and they cross to each other in 22 sec. Find the ratio of their speed ?
(a)    6:7
(b)   7:6
(c)    4:3
(d)   Cannot be determined
(e)   None of these

5. Three partners A, B and C invested money in a business in the ratio of 5:3.5 : 5.5 and ratio of their duration of investment is 2:8/3:1.33. Then what % of total profit will A get?
(a)    30%
(b)   35%
(c)    37.5%
(d)   40%
(e)   None of these

6. The ratio of present ages of son and daughter of a lady is in the ratio of 7:8 and the age of lady is sum total of ages of her daughter and son. If the ratio of ages of son after 3 years and the age of daughter 6 years ago is 4 : 3 then what will be the ratio of the present age of lady and the age of her son after four years?
(a)    4:5
(b)   5:3
(c)    6:5
(d)   9:5
(e)   None of these

7. In a two digit number the digit at unit's place is less than twice the digit at ten's place by 1. And the difference between the number obtained by interchanging its digits and the original number is 50% of the number obtained by adding 1 in original number. What is the original number?
(a)    46
(b)   57
(c)    35
(d)   68
(e)   None of these

8. An alloy contains mixture of two metals A and B in the ratio of 3:5, and the second alloy contains, mixture of same metals in the ratio of 2.33 : 3. In what ratio should be both alloy mixed to make a new alloy containing 42(6/7)% metal A?
(a)    1:2
(b)   3:2
(c)    2:3
(d)   1:6
(e)   None of these

9. The profit earned by a compnay is to be distributed among the managers and officers in the ratio of 7 : 5. If the number of managers and officers is in the ratio of 7 : 12 the amount recieved by each officers is 30,000 what was the total profit earned if the number of managers was 28?
(a)    35 Lakh
(b)   17.5 Lakh
(c)    34.56 Lakh
(d)   19 Lakh
(e)   None of these

10. A shopkeeper offers two successive discounts of 10% and 15% on an article and is still able to earn 53% profit. If he offers only 20% discount what will be his profit percentage?
(a)    70%
(b)   60%
(c)    65%
(d)   80%
(e)   None of these

11. 4 Alcohols of concentrations 75%, 40%, 60%, 50% are mixed in ratio of 1:2:3:4. Find Approximate concentration of water in Final Solution.
(a) 86.92
(b) 46.50
(c) 53.50
(d) 44.50
(e) None of these

12. A rectangular park 305m x 215m has a 5 m wide paved path inside it along each side. Find the cost of pavement of the path at Rs. 9.60 per Square meter.
(a) 24720
(b) 38560
(c) 58960
(d) 48960
(e) None Of these

Solutions :-

Solution:- 1. (b) Rs. 720
Let the price of Cow and Buffalo be X and Y respectively.
Now, ATQ
Cow sold at 16(2/3)% profit = X+16(2/3)% of X = 350X/300 = 7X/6.
Also buffalo at 12(1/2)% loss = X-12(1/2)% of X = 175X/200 = 7X/8.
== > 7X/6 + 7Y/8 = X+Y+30
== > 28X + 21Y = 24X+24Y+720
== > 4X – 3Y = 720…(i)
Also, 7X/8 + 7Y/6 = X+Y
== > -3X + 4Y = 0 …(ii)
Adding (i) and (ii), we get
X+Y = 720


Solution:-2. (a) 14 Hours
New Speed = 7/11 of usual speed
New Time Taken = 11/7 of usual time.
22 = 11/7 of usual time
Usual Time = 22*7/11 = 14 hours.

Solution:-3. (b) 2PM
Let the total work be 180
Efficiency of A = 180/12 = 15/hr.
Efficiency of B = 180/15 = 12/hr.
Efficiency of C = 180/20 = 9/hr.
Now, A worked from 7AM to 10 AM alone before Tap B opened.
Work done in 3 hrs(7-10AM) = 15/hr*3 = 45
Remaining work = 180-45 = 135.
Now, Tap A and B worked together until Tap C opened at 11AM.
Efficiency of A and B together = 27/hr.
Work done in 1 hr (10AM-11AM)= 27.
Remaining Work after 11AM= 108.
Now, all 3 taps are opened after 11AM
Hence, Efficiency of A+B+C = 36/hr
Time taken = 108/36 = 3 hrs.
Therefore, 11AM+3hrs = 14 Hrs= 2PM.

Also can be done in the following way:-
A opened for (7-11)= 4 hrs.
B opened for (10-11) = 1 hr
4/12 + 1/15 + 4t/20 = 1.
20+4+12t = 60
12t = 36
== > t=3hrs.
Hence, 3 hrs after 11AM i.e, at 2PM.

One More easier way

Let The total work be 60
Eficiency of A, B And C will Be 5, 4, and 3 respectively.
Till 11 AM , A worked for 4 hrs , work done = 4* 5 = 20
B worked for 1 hr , Work Done = 1*4= 4
Toatl work done till 11 AM = 24
Remaining work = 60-24= 36
to be done by A+B+C, whose efficiency is 12
Time taken = 36/12= 3 hrs from 11AM i.e., 2PM

Solution:-4. (b) 6:7
Let Speed of the train be X and Ym/s
Length of First train = 28x
Length of Second train = 15y
Also, (28x + 15y) / (x+y) = 22
== > 6x-7y = 0
6x = 7y
x/y = 7/6.

Solution:-5. (c) 37.5%
Money Invested in the ratio = 5:7/2:11/2 = 10:7:11
The Ratio of Duration of Investment = 2:8/3:4/3= 6:8:4= 3:4:2
Ratio of their Profit = 10x3:7x4:11x2 = 30:28:22 = 15:14:11
Profit % of A = 15x100/40 = 37.5%.

Solution:-6. (d) 9:5
Let the present age of Son and Daughter be 7x and 8x respectively.
Then, Age of Lady = 15x
Now, (7x+3)/(8x-6) = 4/3
== > 21x + 9 = 32x-24
== > 11x = 33 == > x= 3
Son’s Age = 21 years
Daughter = 24 years
Lady’s Age = 45 years
Required Ratio = 45/25 = 9/5 = 9:5

Solution:-7. (c) 35
Let the number be 10x+y
Now, ATQ, we have following conditions
(i) y = 2x-1
(ii) 9y-9x = 50%(10x+y+1) = > 9y-9x = 1/2(10x+y+1)
== > 18y-18x = 10x+y+1
== > 17y-28x = 1
Solving (i) and (ii), we get x=3 and y=5
Thus, Number = 10x3+5 = 35

Solution:-8. (d) 1:6
Quantity of A in first alloy = 3/8.
Quantity of A in second Alloy= 7/16.
Let two alloys are mixed in the ratio x:y
Therefore, % of A in new mixture = [(3x/8)+(7x/16)]x100 / [x+y]
But, Given % of A in new mixture = 42(6/7)= (300/7)%
== > [(3x/8)+(7x/16)]x100 / [x+y] = 300/7
== > (6x+7y)/16(x+y) = 3/7
== > 42x+49y = 48x+48y
== > 6x = y  == > x=y = 1/6
Ratio = x:y= 1:6

Solution:-9. (c) 34.56 Lakh
Let the Managers get Rs.X
7X/12*3000 = 7/5 == > X= Rs. 72000
Total Money = 72000*28*12/7 = 34.56 Lakh

Solution:-10. (c) 60%
Total Discount Given = -10-15+150/100 = -25+1.5 = -23.5
Now, Let CP be Rs. 100
SP = Rs. 153
MP = 153x100/(100-23.5)= 153x100/76.5 = 200
Therefore, Marked Price = 200
On Giving 20% discount , SP = 200x80/100 = 160.
SP=160
CP=100
Profit = 60%

Solution :-11 b) 46.50
Water    Alcohol    Ratio    Final Water    Final Alcohol
25    75    1    25        75
60    40    2    120        80
40    60    3    120        180
50    50    4    200        200
        Total    465        535
Now, A+W = 1000
   W= 465
 Water Concentration = 465/1000*100= 46.5%


Solution ;- 12  d) Rs. 48960
Total Area = (305*215) square meter = 65575
Reduced length and breadth from each side = 5m
Hence, total length and breadth reduced by 10m each
New Reduced Area = 295*205 = 60475 square meter
Area of path = 65575-60475 = 5100 square meter
Cost = 5100*9.60 = Rs. 48960