25 February 2025 · Shift 3

LCM and remainders A number that leaves the same remainder 5 with 9, 18 and 23 is exactly 5 more than a common multiple of all three. The LCM of 9, 18 and 23 is 414 (since $18=2\times 9$ and 23 is prime). The largest four-digit multiple of 414 is $414\times 24=9936$, because $414\times 25=10350>9999$. Required number =9936+5=9941. Hence the correct option is (a).

BODMAS simplification By BODMAS the division and the multiplication are done first, and only then the addition and subtraction. $16+8÷4-3\times 4$ =16+2-12 =6 Hence the correct option is (c).

HCF with remainders If the divisor leaves remainder 0 in 1938, it divides 1938 exactly. If it leaves remainder 3 in 2337, it divides 2337-3=2334 exactly. So the required number is the HCF of 1938 and 2334. $1938=2\times 3\times 17\times 19$ and $2334=2\times 3\times 389$, so the HCF $=2\times 3=6$. 6 is larger than the remainder 3, so it is a legitimate divisor. Hence the correct option is (b).

Simple interest Formula: $SI=\frac{P\times R\times T}{100}$. $714=\frac{P\times 7\times 3}{100}$ $P=\frac{714\times 100}{21}$ P=3400 So the principal is ₹3,400, and the correct option is (a).

Percentage of a number "2% of x" means $\frac{2}{100}\times x$. $\frac{2}{100}\times x=300$ $x=\frac{300\times 100}{2}$ x=15000 Hence the correct option is (a).

Mean proportional The mean proportional between a and b is $\sqrt{ab}$. Mean proportional between 15 and 35 $=\sqrt{15\times 35}=\sqrt{525}$. Given: $\sqrt{25\times N}=2\sqrt{525}$. Squaring both sides: $25N=4\times 525=2100$. $N=\frac{2100}{25}=84$ Hence the correct option is (a).

Proportion In a proportion a:b::c:d the product of the extremes equals the product of the means, i.e. $a\times d=b\times c$. Here a=31, b=12, d=156, so $31\times 156=12\times c$. $c=\frac{31\times 156}{12}=31\times 13$ c=403 Hence the correct option is (b).

Compound interest shares Both shares grow at the same rate, so the son whose money is invested for fewer years must start with more. Amount $=P{\left(1+\frac{R}{100}\right)}^n$, and at $R=10\%$ the yearly factor is $\frac{11}{10}$. $A{\left(\frac{11}{10}\right)}^{11}=M{\left(\frac{11}{10}\right)}^{12}$ Cancelling gives $\frac{A}{M}=\frac{11}{10}$, so Arun : Mahesh =11:10. Total =11+10=21 units, and 21 units are ₹1218, so 1 unit is ₹58. Mahesh's share $=10\times 58$, that is ₹580. Hence the correct option is (b).

Average speed The two halves of the journey cover the same distance, so the average speed is the harmonic mean of the two speeds, not their ordinary average. Average speed $=\frac{2xy}{x+y}$ $=\frac{2\times 78\times 91}{78+91}$ $=\frac{14196}{169}$ =84 So the average speed is 84 km/hr, and the correct option is (a).

Weighted average Overall average $=\frac{\mathrm{total}\mathrm{score}\mathrm{of}\mathrm{the}\mathrm{class}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{students}}$. Boys' total $=20\times 75=1500$ Girls' total $=30\times 85=2550$ Overall average $=\frac{1500+2550}{20+30}=\frac{4050}{50}=81$ Hence the correct option is (c).

Profit percentage Profit =1224-1020=204, that is ₹204. Profit percentage is always taken on the cost price: $\frac{204}{1020}\times 100$. $=\frac{1}{5}\times 100=20$ So the profit is $20\%$ and the correct option is (d).

SI and CI difference For 2 years the compound interest beats the simple interest only by the interest earned on the first year's interest. CI-SI=49-42=7 One year's simple interest $=\frac{42}{2}=21$, and ₹7 is one year's interest on this ₹21. $R=\frac{7}{21}\times 100=\frac{100}{3}\%$ $SI=\frac{P\times R\times T}{100}\Rightarrow 42=\frac{P\times \frac{100}{3}\times 2}{100}$ $42=\frac{2P}{3}\Rightarrow P=63$ So the principal is ₹63 and the correct option is (d).

BODMAS with signed numbers By BODMAS, settle the division and the multiplication first and watch the signs. $\left(-60\right)÷\left(-12\right)=+5$ (minus divided by minus is plus) and $\left(-4\right)\times 8=-32$. $\left(-9\right)-\left(-60\right)÷\left(-12\right)+\left(-4\right)\times 8$ =-9-5-32 =-46 Hence the correct option is (d).

Gain stated in selling price Let the selling price of one chair be s and its cost price be c. Gain on 153 chairs =153s-153c, and this is given to be the selling price of 53 chairs, i.e. 53s. $153s-153c=53s\Rightarrow 100s=153c$ $\frac{s}{c}=\frac{153}{100}$, so taking c=100 gives s=153. Profit % $=\frac{s-c}{c}\times 100=\frac{53}{100}\times 100=53$ The gain is 53 chairs' worth of SP, not of CP, so the answer is not 63%; hence the correct option is (a).

Ratio of cylinder volumes Volume of a cylinder $=\pi r^{2}h$, and $\pi$ is common, so the volumes are in the ratio $r^{2}h$. $V_1:V_2=4^2\times 5:5^2\times 2$ $=16\times 5:25\times 2=80:50$ Dividing both by 10, $V_1:V_2=8:5$. Hence the correct option is (b).

Work on alternate days Take the total work as the LCM of 15 and 20, i.e. 60 units. A does $\frac{60}{15}=4$ units a day and B does $\frac{60}{20}=3$ units a day. Working alternately, one pair of days (A then B) finishes 4+3=7 units. In 8 such pairs, i.e. 16 days, $8\times 7=56$ units are done. Work left =60-56=4 units, and the 17th day is A's turn, on which he does exactly 4 units. So the work is completed on the 17th day, with no part of a day left over. Hence the correct option is (d).

Speed, time and delay Over the same distance, speed and time are inversely proportional. New speed : normal speed =1:3, so new time : normal time =3:1. The delay is 3-1=2 units of time, and this is given as 36 minutes. 1 unit $=\frac{36}{2}=18$ minutes. The normal-speed time is 1 unit, i.e. 18 minutes. Hence the correct option is (d).

Income, expenditure and savings Let the savings be 100. "125% more than savings" means expenditure =100+125=225. Income = expenditure + savings =225+100=325. New expenditure $=225\times \frac{86}{100}=193.5$ New savings $=100\times \frac{138}{100}=138$ New income =193.5+138=331.5 Increase =331.5-325=6.5 Increase % $=\frac{6.5}{325}\times 100=2$ Hence the correct option is (d).

Average of weights Mohammad + Ashish + Kiran $=46\times 3=138$ kg. Mohammad + Ashish $=40\times 2=80$ kg. Ashish + Kiran $=42\times 2=84$ kg. Adding the last two totals gives 80+84=164 kg, which counts Ashish twice. So Ashish =164-138=26 kg. Hence the correct option is (b).

Effective discount Let the marked price of one article be ₹1, so the 8 articles the customer carries home are marked at ₹8. Under the scheme he pays for 5 articles only, i.e. ₹5. Discount =8-5=3, taken on the marked price of all 8 articles. Discount % $=\frac{3}{8}\times 100=37.5$ The base is 8, not 5, so the answer is $37.5\%$; hence the correct option is (a).