simplification aptitude questions

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1. A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A. 45 B. 60
C. 75 D. 90

Answer: Option D

Explanation:

 

Let number of notes of each denomination be x.

Then x + 5x + 10x = 480

16x = 480

x = 30.

Hence, total number of notes = 3x = 90.
2. 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. 20 B. 80
C. 100 D. 200

Answer: Option C

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.
3. 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. Rs. 3500 B. Rs. 3750
C. Rs. 3840 D. Rs. 3900

Answer: Option D

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.
4. If a – b = 3 and a2 + b2 = 29, find the value of ab.
A. 10 B. 12
C. 15 D. 18

Answer: Option A

Explanation:

 

2ab = (a2 + b2) – (a – b)2

= 29 – 9 = 20

ab = 10.
5. 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. Rs. 1200 B. Rs. 2400
C. Rs. 4800 D. Cannot be determined
E. None of these

Answer: Option B

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.

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