InfyTQ Algebra Quiz 4

First Faulty chip=1600 \times \frac{21}{5}\times \frac{1}{100}=67.2 =67
Defective chip= 1600\times \frac{19}{3}\times \frac{1}{100}=101.33 =101
So total defective and faulty chips are 67+101=168
Therefore non defective and non-faulty chips are 1600-168=1432

(\frac{15}{30} + 7\frac{2}{7} of \frac{3}{7}) = \frac{1}{2} + \frac{153}{49} = \frac{355}{98}

(5+ 3\frac{ 1}{3})= 5 +\frac{10}{3}=\frac{25}{3}

\frac{\frac{355}{98}}{\frac{25}{3}}=\frac{1065}{ 2450}

Mistake = \frac{1065}{2450} -\frac{400}{2450} = \frac{665}{2450}

\frac{2x}{7} + \frac{4x}{3}+ 2\frac{2}{3} x =21
\frac{90x}{21}=21
x =\frac{49}{10}
Correct answer: Option b

\frac{( a^{2} – b^{2})}{( a +b )^{2}} = 4
\frac{(a+b)(a-b)}{ (a+b) (a+b) }=4
(a-b)=4(a+b)
a=6
b =\frac{-18}{5}

x=\frac{0.00199}{0.001}=1.99
Correct answer: Option d

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 63
9x = 63
x = 7
Required difference = (2x + x) - (2x - x) = 2x = 14
Correct answer: Option d

12 days 70 horses= total work done=12 x 70=840
48 days 30 horses=  total work done= 48 x 30= 1440
Now see here that total work done must be the same but there is a difference. that difference corresponds to the increasing grass/day i.e. work done by grass
work done by grass =1440-840 =600 (this work is done in (48-12=36 days).
work done by grass per day =\frac{600}{36}=\frac{50}{3}
now work done by grass in 12 days= (\frac{50}{3})\times 12=200
actual work = 840 -200 = 640
now work done by grass for 96 days = (\frac{50}{3})\times 96= 1600
total work required to be done = 640 + 1600 = 2240
Horse required = \frac{2240}{96} = 23.33=24
Correct answer: Option a

(\frac{a}{b})^{x-2} = \frac{b}{a}^{x-4}
(\frac{a}{b})^{x-2} = (\frac{a}{b})^-(x-4)
x-2=-x +4
x=3

x= \frac{19128}{3188}

= 6

\frac{1}{\frac{3}{5}}\times 9 \times \frac{1}{\frac{5}{3}}\times 4 = \frac{3}{5}\times 2x

x = 30
Correct answer: Option a