Simplification - Aptitude MCQ Questions and Solutions with Explanations

Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 * 8 * 4) = 160.
∴ 160 * 2.40 + x * 3.20 = 432
⇒ 3.20x = 432 - 384 = 48
⇒ x = 15.
Hence, total hours of work = (160 + 15) = 175.

Explanation 1
$$\eqalign{ & {\text{Let number of children}} = n \cr & {\text{Then, number of books each child will get }} = \frac{n}{8} \cr & {\text{Total books distributed}} = n \times \frac{n}{8} = \frac{{{n^2}}}{8} \cr & {\text{If the number children}} = \frac{n}{2}, \cr & {\text{number of books each child will get}} = 16 \cr & {\text{Total books distributed }} = \frac{n}{2} \times 16 = 8n{\text{ }} \cr & \therefore \frac{{{n^2}}}{8} = 8n \cr & \Rightarrow \frac{n}{8} = 8 \cr & \Rightarrow n = 64 \cr & {\text{Total number of books distributed}} \cr & = 8n = 8 \times 64 = 512 \cr} $$

---

Explanation 2
If number of children was half, each child would have got 16 books.
Therefore, actually each child got $$\frac{{16}}{2}$$ = 8 Books And the number of children is 8 × 8 = 64
Hence, total number of books distributed = 64 × 8 = 512

---

Explanation 3
Let number of children $$ = n$$
Then, number of books each child will get $$ = \frac{n}{8}$$
If the number children $$ = \frac{n}{2}$$,
number of books each child will get $$ = 16$$
More children, less books (indirect proportion). Therefore,
$$\eqalign{ & n : \frac{n}{2} = 16 : \frac{n}{8} \cr & \Rightarrow \frac{{{n^2}}}{8} = 8n \cr & \Rightarrow \frac{n}{8} = 8 \cr & \Rightarrow n = 64 \cr} $$
Therefore, total number of books distributed
= 8n
= 8 × 64
= 512

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

$$\eqalign{ & \frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{\left( {469 \times 174} \right)}} = ? \cr & {\text{We}}\,{\text{ know that}}, \cr & 4ab = {\left( {a + b} \right)^2} - {\left( {a - b} \right)^2} \cr & \therefore \frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{\left( {469 \times 174} \right)}} \cr & = \frac{{4 \times 469 \times 174}}{{469 \times 174}} \cr & = 4 \cr} $$

Suppose their paths cross after x minutes
Then,
11 + 57x = 51 - 63x
⇒ 57x + 63x = 51 - 11
⇒ 120x = 40
⇒ x = $$\frac{1}{3}$$
Number of floors covered by David in $$\frac{1}{3}$$ min.
$$\eqalign{ & = {\frac{1}{3} \times 57} \cr & = 19 \cr} $$
So, their paths cross at (11 + 19) i.e., 30^th floor

$$\eqalign{ & 1 + \frac{1}{{1 + \frac{2}{{2 + \frac{3}{{1 + \frac{4}{5}}}}}}} \cr & = 1 + \frac{1}{{1 + \frac{2}{{2 + \frac{3}{{\frac{9}{5}}}}}}} \cr & = 1 + \frac{1}{{1 + \frac{2}{{2 + \frac{5}{3}}}}} \cr & = 1 + \frac{1}{{1 + \frac{2}{{\frac{{11}}{3}}}}} \cr & = 1 + \frac{1}{{1 + \frac{6}{{11}}}} \cr & = 1 + \frac{1}{{\frac{{17}}{{11}}}} \cr & = 1 + \frac{{11}}{{17}} \cr & = 1\frac{{11}}{{17}} \cr} $$

$$\eqalign{ & 1 + \frac{2}{{1 + \frac{3}{{1 + \frac{4}{5}}}}} \cr & = 1 + \frac{2}{{1 + \frac{3}{{\frac{9}{5}}}}} \cr & = 1 + \frac{2}{{1 + \frac{5}{3}}} \cr & = 1 + \frac{2}{{\frac{8}{3}}} \cr & = 1 + \frac{3}{4} \cr & = \frac{7}{4} \cr} $$

$$\eqalign{ & {\text{According to question}} \cr & \frac{{9|3 - 5| - 5|4| \div 10}}{{ - 3\left( 5 \right) - 2 \times 4 \div 2}} \cr & \Rightarrow \frac{{9 \times 2 - 20 \div 10}}{{ - 15 - 2 \times 2}} \cr & \Rightarrow \frac{{18 - 2}}{{ - 15 - 4}} \cr & \Rightarrow - \frac{{16}}{{19}} \cr} $$

Given,
5 - [4 - {3 - (3 - 3 - 6)}]
= 5 - [4 - {3 - (-6)}]
= 5 - [4 - {3 +6}]
= 5 - [4 - {9}]
= 5 - [4 - 9]
= 5 - [-5]
= 5 + 5
= 10

$$\eqalign{ & \frac{{ - {{\left( {4 - 6} \right)}^2} - 3\left( { - 2} \right) + \left| { - 6} \right|}}{{18 - 9 \div 3 \times 5}} \cr & = \frac{{ - {{\left( { - 2} \right)}^2} - \left( { - 6} \right) + 6}}{{18 - 3 \times 5}} \cr & = \frac{{ - 4 + 6 + 6}}{{18 - 15}} \cr & = \frac{8}{3} \cr} $$