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, PO, UPSC, State-PSC, SSC

[Q] The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(a) 5400
(b) 6400
(c) 2400
(d) 4400

Solution

Answer    (c)
Explanation
----
Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
    and x + 6y = 1600 .... (ii)

Divide equation (i) by 2, we get the below equation. 

=> x +  2y =  800. --- (iii)

Now subtract (iii) from (ii)

 x +  6y = 1600  (-)
 x +  2y =  800  
----------------
      4y =  800
----------------

Therefore, y = 200.

Now apply value of y in (iii)

=>  x + 2 x 200 = 800

=>  x + 400 = 800

Therefore x = 400

Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.

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

[Q] The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(a) 5900
(b) 2900
(c) 3900
(d) 4900

Solution

Answer    (c)
Explanation
----
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.

Then, 10x = 4y   or   y =	5	x.
	2

15x + 2y = 4000

15x + 2 x	5	x = 4000
	2

20x = 4000
x = 200.

So, y =		5	x 200		= 500.
		2

Hence, the cost of 12 chairs and 3 tables = 12x + 3y
    = Rs. (2400 + 1500)
    = Rs. 3900.

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, RBI, clerk, PO, UPSC, State-PSC, Railways, SSC

[Q] The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(a) 5900
(b) 2900
(c) 3900
(d) 4900

Solution

Answer    (c)
Explanation
----
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.

Then, 10x = 4y   or   y =	5	x.
	2

15x + 2y = 4000

15x + 2 x	5	x = 4000
	2

20x = 4000
x = 200.

So, y =		5	x 200		= 500.
		2

Hence, the cost of 12 chairs and 3 tables = 12x + 3y
    = Rs. (2400 + 1500)
    = Rs. 3900.

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

[Q] There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(a) 450
(b) 200
(c) 350
(d) 100

Solution

Answer    (d)
Explanation
----
Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10      x - y = 20 .... (i)
     and x + 20 = 2(y - 20)      x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.

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

[Q] Mohan has Rs. 720 in the denominations of 1-rupee coin, 2-rupee coin and 5-rupee coins. The number of coins of each denomination is equal. What is the total number of coins that he has ?
(a) 660
(b) 270
(c) 560
(d) 470

Solution

Answer    (b)
Explanation
----
Let number of coins of each denomination be x.
Then x + 2x + 5x =720
8x =720
x = 90.
Hence, total number of notes = 3x = (3 x 90) = 270.

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, SBI, RBI, clerk, PO, UPSC, State-PSC, Railways, SSC

[Q] 14+14+14+14=?
(a) 372 / 50
(b) 222 / 50
(c) 72 / 305
(d) 50 / 305

Solution

Answer    (c)
Explanation
----

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