NICL Assistant Online Exam 2015 Question paper

Expression : $$(0.8)^{2.5}\times\frac{(0.8)^{1.5}}{(0.8)^{0.5}}=(0.2)^{3.5}\times2^{?}$$

=> $$(0.8)^{2.5 + 1.5 - 0.5} = (0.2)^{3.5} \times 2^{x}$$

=> $$(0.8)^{3.5} = (0.2)^{3.5} \times 2^{x}$$

=> $$2^x = \frac{(0.8)^{3.5}}{(0.2)^{3.5}}$$

=> $$2^x = (4)^{3.5} = 2^7$$

=> $$x = 7$$

Expression : 6242.52 - 242.2 - ? = 5974.12

=> 6000.32 - x = 5974.12

=> x = 6000.32 - 5974.12 = 26.2

Expression : $$\frac{125^{2}\times\sqrt{(15)}\times5^{3}}{\sqrt{(375)}}=5^{11-?}$$

=> $$\frac{(5)^6 \times \sqrt{15} \times (5)^3}{5 \sqrt{15}} = 5^{11-?}$$

=> $$5^{6 + 3 - 1} = 5^{11-?}$$

=> $$11 - x = 8$$

=> $$x = 11 - 8 = 3$$

Expression : $$\frac{\frac{126}{14}\times?-7\times3}{8^{2}-7\times6+20}=1$$

=> $$\frac{9x - 21}{64 - 42 + 20} = 1$$

=> $$9x - 21 = 42$$

=> $$9x = 42 + 21 = 63$$

=> $$x = \frac{63}{9} = 7$$

Expression : $$34 \times 80 + ?^{2} = 7500 - 4251$$

=> $$2720 + (x)^2 = 3249$$

=> $$(x)^2 = 3249 - 2720 = 529$$

=> $$x = \sqrt{529} = 23$$

Expression : $$42\times4-\sqrt{(625)}-132=\frac{143}{?}$$

=> $$168 - 25 - 132 = \frac{143}{x}$$

=> $$168 - 157 = \frac{143}{x}$$

=> $$x = \frac{143}{11} = 13$$

Expression : $$(2\frac{2}{5}+3\frac{1}{4}-2\frac{7}{8})\times?=222$$

=> $$[(2 + 3 - 2) + (\frac{2}{5} + \frac{1}{4} - \frac{7}{8}) \times x] = 222$$

=> $$(3 + \frac{2}{5} - \frac{5}{8}) \times x = 222$$

=> $$(3 - \frac{9}{40}) \times x = 222$$

=> $$\frac{111}{40} x = 222$$

=> $$x = 222 \times \frac{40}{111}$$

=> $$x = 2 \times 40 = 80$$

Expression : $$\sqrt{(576)}+\sqrt{(1764)}=\sqrt{(?)}$$

=> $$\sqrt{x} = 24 + 42 = 66$$

=> $$x = (66)^2 = 4356$$

Let amount invested by A = $$5x$$ years

=> Amount invested by B = $$9x$$ years

=> Amount invested by C = $$21x$$ years

Thus, ratio of shares A,B and C :

= $$(5x \times 12) : (9x \times 12) : (21x \times 8)$$

= $$5 : 9 : 14$$

Total profit = Rs. 7,084

$$\therefore$$ C's share = $$\frac{14}{5 + 9 + 14} \times 7084$$

= $$14 \times 253 = Rs. 3,542$$

REASONING