19 February 2025 · Shift 2

Fractions and percentage Let the original fraction be $\frac{x}{y}$. New numerator $=x+\frac{40x}{100}=\frac{7x}{5}$ New denominator $=y-\frac{20y}{100}=\frac{4y}{5}$ New fraction $=\frac{7x/5}{4y/5}=\frac{7x}{4y}$ $\frac{7x}{4y}=\frac{7}{4}\times \frac{x}{y}$, so the new fraction is $\frac{7}{4}$ times the original fraction. Hence the correct option is (d).

Average speed Going and returning cover the same distance, so the average speed is the harmonic mean of the two speeds. Formula: average speed $=\frac{2xy}{x+y}$, where x=23 and y=33. $=\frac{2\times 23\times 33}{23+33}=\frac{1518}{56}$ $=\frac{759}{28}=27\frac{3}{28}$ km/h The plain average $\frac{23+33}{2}=28$ is not valid here, because the car travels for different times at the two speeds. Hence the correct option is (a).

LCM of numbers A number divisible by 48, 72, 16 and 15 must be a multiple of their LCM, so the smallest such natural number is the LCM itself. LCM $=2^4\times 3^2\times 5=16\times 9\times 5=720$ Check: $720÷48=15$, $720÷72=10$, $720÷16=45$, $720÷15=48$. Hence the correct option is (b).

LCM of numbers Write each number as a product of primes. LCM = highest power of each prime $=2^3\times 3\times 7\times 13$ $=8\times 3\times 7\times 13=2184$ Hence the correct option is (a).

Profit and selling price Cost price of 100 guavas = ₹1,210 Selling price of 100 guavas = cost price + profit = ₹1,210 + ₹965 = ₹2,175 Selling price of 1 guava $=\frac{2175}{100}=21.75$ Selling price of one dozen $=21.75\times 12=261$ So one dozen guavas sell for ₹261, and the correct option is (c).

Percentage of literates Number of females = 335000 − 214000 = 121000 Total literates = 31% of 335000 = 103850 Literate males = 31% of 214000 = 66340 Literate females = 103850 − 66340 = 37510 Required percentage $=\frac{37510}{121000}\times 100=31\%$ Shortcut: if the whole population and the male group are both 31% literate, the remaining group must also be exactly 31% literate. Hence the correct option is (a).

Fourth proportional If a:b::c:d, then d is the fourth proportional and $a\times d=b\times c$. Here a=2.5, b=9.6 and c=75. $d=\frac{b\times c}{a}=\frac{9.6\times 75}{2.5}$ $=\frac{720}{2.5}=288$ Hence the correct option is (b).

Fourth proportional The fourth proportional to 16, a and 9a is the number d for which 16:a::9a:d. Product of extremes = product of means, so $16\times d=a\times 9a$. $16\times 324=9a^2$ $a^2=\frac{5184}{9}=576$ $a=\sqrt{576}=24$ Hence the correct option is (c).

CI and SI difference For three years, difference $=P\left({\left(1+\frac{R}{100}\right)}^3-1-\frac{3R}{100}\right)$ The same formula in short form: difference $=\frac{P{R}^2\left(300+R\right)}{{10}^6}$ Putting R=10: difference $=\frac{P\times 100\times 310}{{10}^6}=\frac{31P}{1000}$ $\frac{31P}{1000}=217$ $P=\frac{217\times 1000}{31}=7000$ So the principal is ₹7,000, and the correct option is (d).

Averages of weights Total weight of the three $=46\times 3=138$ kg Mohan + Mohammad $=39\times 2=78$ kg Mohammad + Ashish $=47\times 2=94$ kg Ashish =138-78=60 kg Mohammad =94-60=34 kg Hence the correct option is (d).

Compound interest and ratio Under compound interest an amount X becomes $X{\left(1+\frac{4}{100}\right)}^n$ in n years. Nitin's share grows for 19 years and Pravin's for 20 years, and the two amounts turn out equal. $N{\left(\frac{26}{25}\right)}^{19}=P{\left(\frac{26}{25}\right)}^{20}$ $\frac{N}{P}=\frac{26}{25}$, so Nitin : Pravin =26:25. 26+25=51 units = ₹1,224, so 1 unit $=\frac{1224}{51}=24$, that is ₹24. Pravin's share $=25\times 24=600$ So Veer gave Pravin ₹600, and the correct option is (c).

Average speed Take the whole journey as 8 units of distance. Time for the first $\frac{3}{8}$ part $=\frac{3}{60}$ h; time for the remaining $\frac{5}{8}$ part $=\frac{5}{40}$ h. Total time $=\frac{1}{20}+\frac{1}{8}=\frac{2+5}{40}=\frac{7}{40}$ h Average speed = total distance ÷ total time $=\frac{8}{7/40}=\frac{320}{7}$ $\frac{320}{7}=45.71\dots \approx 46$ km/hr Hence the correct option is (b).

Surface area of a sphere Curved surface area of a sphere $=4\pi r^2$ $4\times \frac{22}{7}\times r^2=9856$ $r^2=\frac{9856\times 7}{88}=784$ $r=\sqrt{784}=28$ cm Diameter $=2r=2\times 28=56$ cm The answer is asked in metres, so 56 cm = 0.56 m (not 5.6 m). Hence the correct option is (d).

Profit percentage Let the cost price of one pen be x and its selling price be y. 12x=9y, so $\frac{y}{x}=\frac{12}{9}=\frac{4}{3}$. Take CP = ₹3 and SP = ₹4 per pen, so the profit is ₹1 per pen. Profit percentage $=\frac{1}{3}\times 100=33\frac{1}{3}\%$ Hence the correct option is (c).

Simple interest Formula: simple interest $=\frac{P\times R\times T}{100}$ $487=\frac{P\times 5\times 2}{100}$ $P=\frac{487\times 100}{10}=4870$ So the principal is ₹4,870, and the correct option is (a).

Work done in rotation Take the total work as the LCM of 25, 30, 36 and 40, that is 1800 units. One day's work: P = 72, Q = 60, R = 50 and S = 45 units. The rotation is Q, S, P, R, so one cycle of 4 days does 60+45+72+50=227 units. $227\times 7=1589$ units, so 7 complete cycles (28 days) leave the work unfinished. Remaining work =1800-1589=211 units Day 29 (Q) leaves 211-60=151; day 30 (S) leaves 151-45=106; day 31 (P) leaves 106-72=34. R does 50 units a day, so R needs $\frac{34}{50}=\frac{17}{25}$ of the 32nd day. Total time $=31+\frac{17}{25}=31\frac{17}{25}$ days Hence the correct option is (b).

BODMAS simplification Apply BODMAS: division and multiplication first, then addition and subtraction. $\left(-60\right)÷\left(-15\right)=4$ and $\left(-2\right)\times 7=-14$ (-9)-4+(-14) =-13-14=-27 Hence the correct option is (a).

Discount and cost price Selling price $=950\times \frac{100-20}{100}=950\times \frac{80}{100}=760$ Given: selling price = 2.5 × cost price Cost price $=\frac{760}{2.5}=304$ So the cost price is ₹304, and the correct option is (b).

BODMAS simplification BODMAS: solve $÷$ and $\times$ before + and -. $9÷3=3$ and $3\times 3=9$ 16+3-9=10 Hence the correct option is (b).

Speed, time and distance For a fixed distance, time is inversely proportional to speed. The new speed is $\frac{1}{4}$ of the normal speed, so the new time is 4 times the normal time. Extra time =4t-t=3t, and this extra time is 54 minutes. 3t=54, so t=18 So at his normal speed Kamal takes 18 minutes, and the correct option is (d).