Simplification question for IBPS, SBI, RBI, clerk, PO, Railways, SSC

[Q] In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows.
(a) 17
(b) 33
(c) 24
(d) 14

Solution

Answer    (d)
Explanation
----
Let the number of ducks be d
and number of cows be c

Then, total number of legs = 2d + 4c = 2(d + 2c)

total number of heads = c + d

Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 28 + 2(c + d)
=> d + 2c = 14 + c + d
=> 2c = 14 + c
=> c = 14

i.e., total number of cows = 14

Simplification question for IBPS, SBI, RBI, clerk, PO, Railways, SSC

[Q] A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
(a) 62
(b) 26
(c) 36
(d) 63

Solution

Answer    (b)
Explanation
----
Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
  and 2x + 4y = 140      x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.

Simplification question for IBPS, SBI, RBI, clerk, PO, Railways, SSC

[Q] In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(a) 475
(b) 275
(c) 375
(d) 175

Solution

Answer    (d)
Explanation
----
Assume the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.

Simplification question for IBPS, SBI, RBI, clerk, PO, Railways, SSC

[Q] In a class there are equal number of boys and girls. Eight girls left the room, leaving twice as many boys as girls in the room . What was the total number of boys and girls present in the room initially?
(a) 14
(b) 32
(c) 33
(d) 24

Solution

Answer    (b)
Explanation
----
Assume that initial number of boys = initial number of girls = x

2(x-8) = x
=> 2x - 16 = x
=> x = 16

Total number of boys and girls = 2x = 2 × 16 = 32

Simplification question for IBPS, SBI, RBI, clerk, PO, UPSC, State-PSC, Railways, SSC

[Q] If a - b = 3 and a² + b² = 29, find the value of ab.
(a) 40
(b) 10
(c) 30
(d) 20

Solution

Answer    (b)
Explanation
----
2ab = (a² + b²) - (a - b)²
   = 29 - 9 = 20
   ab = 10.

Simplification question for IBPS, SBI,PO, RBI, clerk, Railways, SSC

[Q] b - [b -a -b - {a -b} + 2a]= ?
(a) 1
(b) 0
(c) 3
(d) 2

Solution

Answer    (b)
Explanation
----
b - [b -a -b - {a -b} + 2a]

= b - [b -a -b - a +b + 2a]

= b - [b]

= b - b

= 0

Simplification question for IBPS-clerk, Railways, SSC

[Q] 213+312+414 = ?
(a) 1
(b) 2
(c) 3
(d) 4

Solution

Answer    (a)
Explanation
----
213+312+414=73+72+174=(28+42+51)12=12112=10112

Simplification question for IBPS, SBI, RBI, clerk, PO, UPSC, State-PSC, Railways, SSC

[Q] (723+1992)2−(723−1992)2723×1992          = ?
(a) 1
(b) 2
(c) 3
(d) 4

Solution

Answer    (d)
Explanation
===(723+1992)2−(723−1992)2723×1992(a+b)2−(a−b)2ab(where a = 723 and b = 1992)a2+2ab+b2−(a2−2ab+b2)ab4ab4=4