6 February 2025 · Shift 2

Simple interest - principal Simple interest depends on the principal, the rate and the time together. Formula: $SI=\frac{P\times R\times T}{100}$ Substituting SI=378, R=9 and T=5: $378=\frac{P\times 9\times 5}{100}$ $378=\frac{45P}{100}$ $P=\frac{378\times 100}{45}$ P=840 So the correct option is (a).

Successive discounts Successive discounts are multiplied one after the other, never added. Let the bill amount be M. After the first discount the price is $M\times \frac{70}{100}$. After the second discount it is $M\times \frac{70}{100}\times \frac{80}{100}=\frac{56M}{100}$. $\frac{56M}{100}=840$ $M=\frac{840\times 100}{56}$ M=1500 So the correct option is (d).

Trains crossing - same direction Moving in the same direction, the relative speed is the difference of the two speeds. Relative speed =75-30=45 km/h 45 km/h $=45\times \frac{5}{18}=12.5$ m/s While crossing, the faster train covers the sum of the two lengths. Let the slow train be x m long: $950+x=12.5\times 108$ 950+x=1350 x=1350-950=400 So the correct option is (a).

BODMAS simplification By BODMAS, division and multiplication are done before addition and subtraction. $16+10÷5-2\times 4$ $=16+2-2\times 4$ =16+2-8 =18-8 =10 So the correct option is (a).

Mean proportional The mean proportional between a and b is $\sqrt{ab}$. Here a=x and b=4x, so $\sqrt{x\times 4x}=456976$ $\sqrt{4x^2}=456976$ 2x=456976 $x=\frac{456976}{2}$ x=228488 So the correct option is (c).

Income, expenditure and savings Income = expenditure + savings, so find the expenditure before changing anything. Savings $=\frac{23}{100}\times 75400=17342$ Expenditure =75400-17342=58058 New income $=75400\times \frac{127}{100}=95758$ New expenditure $=58058\times \frac{150}{100}=87087$ New savings =95758-87087=8671 Change =17342-8671=8671, and the new savings are smaller. So the savings decrease by ₹8,671 and the correct option is (a).

Surface area of a sphere Radius $r=\frac{21}{2}=10.5$ cm Surface area of a sphere $=4\pi r^2$ $=4\times \frac{22}{7}\times 10.5\times 10.5$ $=4\times 22\times 1.5\times 10.5$ $=88\times 15.75$ =1386 So the surface area is 1386 sq. cm and the correct option is (b).

Averages of pairs Turn every average into a total, because totals can be subtracted. Mahesh + Ram + Anwar $=46\times 3=138$ Mahesh + Ram $=39\times 2=78$ Ram + Anwar $=49\times 2=98$ Anwar =138-78=60 Ram =98-60=38 So Ram weighs 38 kg and the correct option is (c).

Percentage of a number $2\%$ of x means $\frac{2}{100}\times x$. $\frac{2}{100}\times x=276$ $x=\frac{276\times 100}{2}$ $x=138\times 100$ x=13800 So the correct option is (b).

BODMAS with brackets Open the innermost bracket first, then the curly bracket, then the square bracket. 19-15=4, so the fraction becomes $\frac{4}{4}=1$ Inside the curly bracket: $3÷3\times 1=1\times 1=1$ Inside the round bracket: $27\times 3=81$ $\left(81\times 1\right)$ =81 So the correct option is (c).

Profit as a part of selling price Profit per cent is always taken on the cost price, so find the cost price first. Let the selling price of one chair be S. Total selling price =152S and profit =76S Cost price =152S-76S=76S Profit$\%=\frac{76S}{76S}\times 100$ $=100\%$ So the correct option is (a).

LCM and HCF relation For any two numbers, LCM $\times$ HCF = product of the numbers. $4158\times 54=378\times N$ $N=\frac{4158\times 54}{378}$ $\frac{4158}{378}=11$, so $N=11\times 54$ N=594 So the correct option is (c).

Compound interest - equal amounts Anil's money is invested for one year longer, so his share must be the smaller one. Let Anand get A and Anil get B. The two amounts are equal: $A\times {\left(\frac{104}{100}\right)}^{17}=B\times {\left(\frac{104}{100}\right)}^{18}$ $\frac{A}{B}=\frac{104}{100}=\frac{26}{25}$ Total parts =26+25=51 One part $=\frac{1224}{51}=24$ Anil's share $=25\times 24=600$ So Manoj gave ₹600 to Anil and the correct option is (c).

Trains crossing - opposite directions In opposite directions the relative speed is the sum of the two speeds. Relative speed =50+110=160 km/h 160 km/h $=160\times \frac{5}{18}=\frac{400}{9}$ m/s While crossing, the trains together cover the sum of their lengths. $500+x=\frac{400}{9}\times 12=\frac{4800}{9}$ 500+x=533.33 x=533.33-500=33.33 So the correct option is (a).

BODMAS with brackets Solve the innermost bracket first, then the curly bracket, then the square bracket. 9-5=4 Inside the curly bracket: $\frac{96}{8}+\frac{11}{4}\times 4$ =12+11=23 Inside the round bracket: $63÷9=7$ $\left(7\times 23\right)=161$ So the correct option is (c).

Average of four values The average is the total of the four months divided by 4. Sum =28312+32252+25012+33500 =119076 Average $=\frac{119076}{4}$ =29769 So the average expenditure is ₹29,769 and the correct option is (b).

Selling price from profit per cent A profit of $26\%$ makes the selling price $126\%$ of the cost price. SP $=500\times \frac{100+26}{100}$ $=500\times \frac{126}{100}$ $=5\times 126$ =630 So he should sell it for ₹630 and the correct option is (b).

Time and work - efficiency ratio Compare the two workers on the same footing: work done divided by time taken. Let B do 2 units of work in 4 days; then A does 1 unit in 3 days. Efficiency of A $=\frac{1}{3}$ and efficiency of B $=\frac{1}{2}$ A : B $=\frac{1}{3}:\frac{1}{2}=2:3$ Taking the efficiencies as 2 and 3, together they do 2+3=5 units a day. Total work $=5\times 66=330$ units Days taken by B alone $=\frac{330}{3}=110$ So the correct option is (c).

Third proportional If c is the third proportional of a and b, then a:b=b:c. So $c=\frac{b^2}{a}$ $c=\frac{42\times 42}{36}$ $c=\frac{1764}{36}$ c=49 So the correct option is (a).

Compound interest - equal amounts Varun's money grows for one year longer, so Varun must start with less. Let Raj get R and Varun get V. The amounts are equal: $R\times {\left(\frac{108}{100}\right)}^{15}=V\times {\left(\frac{108}{100}\right)}^{16}$ $\frac{R}{V}=\frac{108}{100}=\frac{27}{25}$ Total parts =27+25=52 One part $=\frac{1612}{52}=31$ Raj's share $=27\times 31=837$ So Ashok gave ₹837 to Raj and the correct option is (b).