RPF 16 Jan 2019

Production of company Z in 2001 (in thousands) = 83

Production of company Y in 2002 (in thousands) = 86

=> Required difference (in thousands) = $$86-83=3$$

=> Ans - (B)

Numbers which are divisible by 24, must first be divisible by 3 and also by 8. Checking divisibility by 8.

153228, 158322 and 153822 are not divisible by 8, so only third number is divisible by 3 and 8.

Thus, 158232 is divisible by 24.

=> Ans - (C)

Marks obtained = 76 + 92 + 34 + 38 = 240

Maximum marks = 120 + 130 + 70 + 80 = 400

$$\therefore$$ Overall percentage obtained by him = $$\frac{240}{400}\times100=60\%$$

=> Ans - (A)

Expression : $$\sqrt{(700 - x)} = \sqrt{(689 - \sqrt{169})}$$

=> $$(700-x)=689-13=676$$

=> $$x=700-676=24$$

=> Ans - (D)

Production of the company X in 2002 = 81

Production of the company X in 2005 = 84

=> Increase in production = $$\frac{84-81}{81}\times100\approx3.70\%$$

=> Ans - (B)

Expression : $$\sqrt{(1057 - \sqrt{(1109 - \sqrt{(450 - \sqrt{2500})})})}$$

= $$\sqrt{(1057 - \sqrt{(1109 - \sqrt{(450 - 50)})})}$$

= $$\sqrt{(1057 - \sqrt{(1109 - \sqrt{400})})}$$

= $$\sqrt{(1057 - \sqrt{(1109 - 20)})}$$

= $$\sqrt{(1057 - \sqrt{(1089})}$$

= $$\sqrt{1057 - 33}=\sqrt{1024}=32$$

=> Ans - (B)

Quantity of milk in 189 litres mixture = $$\frac{3}{(3+4)}\times189=81$$ litres

=> Quantity of water = $$189-81=108$$ litres

Let $$x$$ litres of water is to be added.

=> $$\frac{81}{108+x}=\frac{3}{5}$$

=> $$405=324+3x$$

=> $$3x=405-324=81$$

=> $$x=\frac{81}{3}=27$$

$$\therefore$$ Quantity of water to be further added is 27 litres.

=> Ans - (D)

Let usual speed = $$10$$ m/min and usual time taken = $$t$$ min

=> New speed = $$9$$ m/min and new time = $$(t+27)$$ min

Also, speed is inversely proportional to time.

=> $$\frac{10}{9}=\frac{t+27}{t}$$

=> $$10t=9t+243$$

=> $$10t-9t=t=243$$

$$\therefore$$ Usual time taken = 243 minutes

=> Ans - (A)

Let side of cube be $$a$$ cm

=> Diagonal = $$\sqrt{a^2+a^2+a^2}=47\sqrt3$$

=> $$\sqrt3a=47\sqrt3$$

=> $$a=47$$ cm

Let height of cuboid = $$h$$ cm, length, $$l=47$$ cm and breadth, $$b=23.5$$ cm

According to ques, Volume of cuboid = Volume of cube

=> $$lbh=a^3$$

=> $$47\times23.5\times h=(47)^3$$

=> $$h=\frac{47\times47}{23.5}=94$$ cm

=> Ans - (A)

Rate of interest = 6% and time period = 2 years

Let principal sum = Rs. $$P$$

Also, difference between compound interest and simple interest for 2 years = $$P(\frac{r}{100})^2$$

=> $$P(\frac{6}{100})^2=234$$

=> $$P=234\times\frac{10000}{36}$$

=> $$P=Rs.$$ $$65,000$$

=> Ans - (D)