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, 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, 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