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## Simplification Problems- Aptitude Questions and Answers:-

This is aptitude on Simplification Problems Question and answers with explanation for different interviews and competitive and entrance exams.

**1) . A man has Rs. 900 in the denominations of ten-rupee notes, twenty rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?**

A. 20

B. 25

C. 15

D. 35

Answer: Option **C**
Explanation: Let number of notes of each denomination be a.
Then 10a + 20a = 900
30a = 900
a = 30.
Hence, total number of notes = 2a = 15.

**2) If x – y = 5 and x2 + y2 = 51, find the value of xy.**

A. 11

B. 13

C. 16

D. 19

Answer: Option **A**
Explanation:
2xy = (x2 + y2) - (x - y)2
2xy = 51 - 25
2xy = 26
xy = 13

**3) The price of 12 chairs is equal to that of 4 tables. The price of 16 chairs and 2 tables together is Rs. 4400. The total price of 10 chairs and 4 tables is:**
A. Rs. 3600

B. Rs. 3300

C. Rs. 4400

D. Rs. 3900

Answer: Option **C**
Explanation:
Let the cost of a chair and that of a table be Rs. A and Rs. B respectively.
Then, 12A = 4B or B = 3A
16A + 2B = 4000
6A + 2 * 3A = 4400
22A = 4400
A= 200.
So, B = 3 * 200
B= 600
Hence, the cost of 10 chairs and 4 tables = 10A + 4B
= Rs. (2000 + 2400)
= Rs. 4400

**4) To fill a tank, 30 buckets of water is required. How many buckets of water shall be required to fill the same tank if the capacity of the bucket is reduced to one-fifth of its present ?**
A. 15

B. 50

C. 150

D. None of these

Answer: Option **C**
Explanation:
Let the capacity of 1 bucket = a.
Then, the capacity of tank = 30a.
New capacity of bucket =1/5 a
Required number of buckets = 30a / (a/5)
= 150a / a
= 150

**5) A woman has some dogs and cats. If the number of heads be 60 and the number of feet equals 120, then the number of dogs will be:**
A. 55

B. 45

C. 50

D. 60

Answer: Option **D**
Explanation:
Let the number of dogs be 'a' and the number of cats be 'b'.
Then, a + b = 60 .... (i)
and 2a + 4b = 120
a + 2b = 60 .... (ii)
Solving (i) and (ii) we get: a = 60, b = 40.
The required answer = 60.

6. 6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = ?

A. 150 1/3

B. 150 2/3

C. 149 2/3

D. 149 1/3

Answer: Option **B**
Explanation:
6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = 20/3 * 48/5 * 7/3 + 4/3
= 448/3 + 4/3 = 452/3 = 150 2/3

7.(22 * 495 + 891 * 44) / (33 * 176 + 55 * 264) = ?

A. 1

B. 2

C. 69/28

D. 66/17

Answer: Option **C**
Explanation:
(22 * 495 + 891 * 44) / (33 * 176 + 55 * 264) = (22 * 33 * 15 + 9 * 99 * 2 * 22) / (33 * 22 * 8 + 5 * 11 * 22 * 12)
= (22 * 33 * 15 + 22 * 33 * 54) / (33 * 22 * 8 + 33 * 22 * 20)
= [22 * 33(15 + 54)] / [33 * 22(8 + 20)] = 69/28

8.8.008 + 0.8 + 80.8 + 800.8 + 0.08 = ?

A. 888.888

B. 889.688

C. 890.488

D. 980.488

Answer: Option **C**
Explanation:
8.008 + 0.8 + 80.8 + 800.8 + 0.08
= 8 + 0.008 + 0.8 + 80 + 0.8 + 800 + 0.8 + 0.08
= 8 + 80 + 800 + 0.008 + 0.08 + 0.8 + 0.8 + 0.8
= 888 + 2.488 = 890.488

9.64309 – 8703 + 798 – 437 = ?

A. 55606 B. 55697 C. 55967 D. 73373

Answer: Option **C**
Explanation:
64309 - 8703 + 798 - 437 => 65107 - 9140 = 55967

10.Which of the following groups of fractions is in descending order?

A. 8/15, 9/13, 6/11

B. 8/15, 6/11, 9/13

C. 9/13, 6/11, 8/15

D. 6/11, 8/15, 9/13

Answer: Option **C**
Explanation:
The fractions considered are 8/15 9/13 6/11
To compare them we make the denominators the same. So the fractions are
(8 * 13 * 11)/2145, (9 * 15 * 11)/2145 and (6 * 15 * 13)/2145
1144/2145, 1485/2145 and 1170/2145
so in descending order the fractions will be
1485/2145, 1170/2145 and 1144/2145 i.e., 9/13 , 6/11 , 8/15

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