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Simplification - Aptitude MCQ Questions and Solutions with Explanations

Simplification MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Simplification with easy and logical explanations. Simplification MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc.

Each section contains 100 MCQs on Simplification .
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 ?
Discuss
Answer & Solution
Answer: Option D
Solution:
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:
Discuss
Answer & Solution
Answer: Option C
Solution:
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:
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{cost}}\,{\text{of}}\,{\text{a}}\,{\text{chair}}\,{\text{and}}\,{\text{that}}\,{\text{of}}\,\,{\text{table}} \cr & \,{\text{be}}\,Rs.\,x\,{\text{and}}\,Rs.\,y\,{\text{respectively}}. \cr & {\text{Then}},\,10x = 4y\,\,\,or\,\,\,y = \frac{5}{2}x \cr & \therefore 15x + 2y = 4000 \cr & \Rightarrow 15x + 2 \times \frac{5}{2}x = 4000 \cr & \Rightarrow 20x = 4000 \cr & \therefore x = 200 \cr & {\text{So}},\,y = {\frac{5}{2} \times 200} = 500 \cr & {\text{Hence,}}\,{\text{the}}\,{\text{cost}}\,{\text{of}}\,{\text{12}}\,{\text{chairs}}\,{\text{and}}\,{\text{3}}\,{\text{tables}} \cr & = 12x + 3y \cr & = Rs.\,\left( {2400 + 1500} \right) \cr & = Rs.\,3900 \cr} $$
4
If a - b = 3 and a2 + b2 = 29, find the value of ab.
Discuss
Answer & Solution
Answer: Option A
Solution:
2ab = (a2 + b2) - (a - b)2
2ab = 29 - 9
2ab = 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 ?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{price}}\,{\text{of a}}\,{\text{saree}}\,{\text{and}}\,{\text{a}}\,{\text{shirt}} \cr & \,{\text{be}}\,Rs.\,x\,{\text{and}}\,Rs.\,y\,{\text{respectively}}. \cr & {\text{Then,}}\,2x + 4y = 1600\,....(i) \cr & \,\,\,\,\,\,\,\,\,\,\,{\text{and}}\,x + 6y = 1600\,....(ii) \cr & {\text{Divide}}\,{\text{equation}}\,(i)\,by\,2, \cr & {\text{we}}\,{\text{get}}\,{\text{the}}\,{\text{below}}\,{\text{equation}}. \cr & = > \,x + 2y = 800\,\, - - - (iii) \cr & {\text{Now}}\,{\text{subtract}}\,(iii)\,{\text{from}}\,(ii) \cr & x\,\, + \,\,\,\,6y\,\, = \,\,1600\,\,\,( - ) \cr & x\,\, + \,\,\,\,2y\,\, = \,\,\,\,\,\,\,800 \cr & - - - - - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4y\,\, = \,\,\,\,\,\,800 \cr & - - - - - - - - - - \cr & {\text{Therefore}},\,y = 200 \cr & {\text{Nowapply}}\,{\text{value}}\,{\text{of}}\,y\,{\text{in}}\,(iii) \cr & = > x + 2 \times 200 = 800 \cr & = > x + 400 = 800 \cr & {\text{Therefore}}\,x = 400 \cr & {\text{Solving}}\,(i)\,{\text{and}}\,(ii)\,{\text{we}}\,{\text{get}}\, \cr & x = 400,\,y = 200 \cr & \therefore {\text{Cost}}\,{\text{of}}\,{\text{12}}\,{\text{shirts}} \cr & = Rs.\,\left( {12 \times 200} \right) \cr & = Rs.\,2400 \cr} $$
6
A sum of Rs. 1360 has been divided among A, B and C such that A gets $$\frac{2}{3}$$ of what B gets and B gets $$\frac{1}{4}$$ of what C gets. B's share is:
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{Let}}\,C's\,{\text{share}} = Rs.\,x \cr & \text{Then,}\,B's\,{\text{share}} = \,Rs.\,\frac{x}{4}, \cr & A's\,{\text{share}} = Rs.\,\left( {\frac{2}{3} \times \frac{x}{4}} \right) = Rs.\,\frac{x}{6} \cr & \therefore \frac{x}{6} + \frac{x}{4} + x = 1360 \cr & \Rightarrow \frac{{17x}}{{12}} = 1360 \cr & \Rightarrow x = \frac{{1360 \times 12}}{{17}} = Rs.\,960 \cr & {\text{Hence}},\,B's\,{\text{share}} = Rs.\,\left( {\frac{{960}}{4}} \right) \cr & = Rs.\,240 \cr} $$
7
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{Let}}\,{\text{saving}}\,{\text{in}}\,{\text{N}}{\text{.S}}{\text{.C}}\,{\text{and}}\,{\text{P}}{\text{.P}}{\text{.F}}{\text{.}}\,{\text{be}}\, \cr & Rs.\,x\,{\text{and}}\,Rs.\,\left( {150000 - x} \right){\text{respectively}}. \cr & {\text{Then}},\,\frac{1}{3}x = \frac{1}{2}\left( {150000 - x} \right) \cr & \Rightarrow \frac{x}{3} + \frac{x}{2} = 75000 \cr & \Rightarrow \frac{{5x}}{6} = 75000 \cr & \Rightarrow x = \frac{{75000 \times 6}}{5} = 90000 \cr & \therefore {\text{Savings}}\,{\text{in}}\,{\text{Public}}\,{\text{Provident}}\,{\text{Fund}} \cr & = Rs.\,\left( {150000 - 90000} \right) \cr & = Rs.\,60000 \cr} $$
8
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{total}}\,{\text{number}}\,{\text{of}}\,{\text{shots}}\,{\text{be}}\,x. \cr & {\text{Then,}}\,{\text{Shots}}\,{\text{fired}}\,{\text{by}}\,{\text{A}} = \frac{5}{8}x \cr & {\text{Shots}}\,{\text{fired}}\,{\text{by}}\,{\text{B}} = \frac{3}{8}x \cr & {\text{Killing}}\,{\text{shots}}\,{\text{by}}\,{\text{A}} \cr & = \frac{1}{3}{\text{of}}\frac{5}{8}x = \frac{5}{{24}}x \cr & {\text{Shots}}\,{\text{missed}}\,{\text{by}}\,{\text{B}} \cr & = \frac{1}{2}{\text{of}}\,\frac{3}{8}x = \frac{3}{{16}}x \cr & \therefore \frac{{3x}}{{16}} = 27\,{\text{or}}\,x = {\frac{{27 \times 16}}{3}} = 144 \cr & {\text{Birds}}\,{\text{killed}}\,{\text{by}}\,{\text{A}} \cr & = \frac{{5x}}{{24}} = {\frac{5}{{24}} \times 144} = 30 \cr} $$
9
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Original}}\,{\text{share}}\,{\text{of}}\,{\text{1}}\,{\text{person}} = \frac{1}{8} \cr & {\text{New}}\,{\text{share}}\,{\text{of}}\,{\text{1}}\,{\text{person}} = \frac{1}{7} \cr & {\text{Increase}} = {\frac{1}{7} \times \frac{1}{8}} = \frac{1}{{56}} \cr & \therefore {\text{Required}}\,{\text{fraction}} \cr & = \frac{{ {1/56} }}{{ {1/8} }} = {\frac{1}{{56}} \times \frac{8}{1}} = \frac{1}{7} \cr} $$
10
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{capacity}}\,{\text{of}}\,{\text{1}}\,{\text{bucket}} = x \cr & {\text{Then,}}\,{\text{the}}\,{\text{capacity}}\,{\text{of}}\,{\text{tank}} = 25x \cr & {\text{New}}\,{\text{capacity}}\,{\text{of}}\,{\text{bucket}} = \frac{2}{5}x \cr & \therefore {\text{Required}}\,{\text{number}}\,{\text{of}}\,{\text{buckets}} \cr & = \frac{{25x}}{{\left( {2x/5} \right)}} \cr & = {25x \times \frac{5}{{2x}}} \cr & = \frac{{125}}{2} \cr & = 62.5 \cr} $$