Ans : As 738A6 A is divisible by 11.
We know A + A + 3 = 6 + 8 + 7
We know A = 9
Very important Maths questions for SSC CGL
Q. The east positive integer that should be subtracted from 3011 * 3012 so that the difference is perfect square is-
a. 3009
b. 3010
c. 3011
d. 3012
Ans : We know that 3011 * 3012 = 3011 (3011 + 1)
= (3011)2 + 3011
We know Required least number = 3011
Q. P, Q, R are employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q, in rupees, is-
a. 2850
b. 3750
c. 2750
d. 1000
Ans : Work done by Q = 19/23 + 8/23 – 1
4/23
We know Wage of Q = 4/23 * 5750
= Rs. 1000
Q. A can do a piece of work in 24 day, B in 32 days and C in 64 days. All begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?
a. 15
b. 20
c. 18
d. 30
Ans : Work done by A = 6/24 = ¼
Work done by B = (x-6)/32
(where x is no. of days in which work is competed)
We know that ¼ + x – 6/32 + x/64 = 1
We know 16 + 24 – 12 + x /64 = 1
We know 3x + 4 = 64
We know x = 60/3 = 20 days
Q. The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-
a. 1
b. 2
c. 3
d. 4
: The square root of
[(0.75)3/1 – 0.75 + {0.75 + (0.75)2 + 1}]
= ?1.6875 + 2.3125
=?4
= 2
Q. Given that ?4096 = 64, the value of ?4096 + ?40.96 +?0.004096 is-
a. 70.4
b. 70.464
c. 71.104
d. 71.4
Ans : Given Exp. = ?4096 + ?40.96 +?0.004096
= 64 + 6.4 + 0.064
= 70.464
Q. By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is-
a. 5 : 3
b. 3 : 5
c. 3 : 4
d. 4 : 3
Ans : Let of M.P. be Rs. x.
We know S.P. = Rs.3x/4
and C.P. = 3x/4 * 100/125
= Rs.3x/5
We know required ratio = x: 3x/5
= 5:3
Q. A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, the monthly income of B is-
a. Rs.7,000
b. Rs.14,000
c. Rs.5,000
d. Rs.10,000
Ans : Let the monthly income of B be Rs. x.
We know Monthly income of A = Rs. 2x and
Saving of A =5000 * 4/(4 + 1)
= Rs. 4000
Saving of B = Rs.1000
We know that 2x – 4000/x-1000 = 5/3
=> 6x – 12000 = 5x – 5000
We know x = Rs.7000
Q. The ratio of the sum of two numbers and their difference is 5:1. The ratio of the greater number to the smaller number is-
a. 2 : 3
b. 3 : 2
c. 5 : 1
d. 1 : 5
Ans : Let the numbers be x and y.
We know that x + y/ x – y = 5/1
=> 5x – 5y = x + y
=> 4x = 6y
=> x/y = 6/4
x : y = 3 : 2
Q. A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours respectively, and C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be empty at-
a. 7.12 p.m.
b. 7.15 p.m.
c. 7.10 p.m.
d. 7.18 p.m.
Ans : Let the cistern be emptied at x p.m.
We know that x -3/3 + x – 4/4 = x – 5/1
=> 4x – 12 + 3x – 12/12 = x – 5/1
=> 7x – 24 = 12x – 60
=> 5x = 36
We know x = 36/5
= 7 hr. + 12 min.
= 7.12 p.m.
Q. If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if A and B work together. How many days would they take to complete the work if both of them worked together?
a. 10 days
b. 12 days
c. 6 days
d. 8 days
Let x days are taken when they work together.
We know Time taken by A to complete the work = (x + 4) days
And Time taken by B to complete the work = (x + 16) days
We know that 1/x = 1/x + 4 + 1/x + 16
We know 1/x = x + 16 + x + 4/(x + 4) (x +16)
We know 2×2 + 20x = x2 + 20x +64
We know x2 = 64 (8)2
We know x = 8 days