19 February 2025 · Shift 1

BODMAS order BODMAS: finish every division and multiplication before any addition or subtraction. $12÷3=4$ and $3\times 4=12$. $16+12÷3-3\times 4=16+4-12$ =20-12=8 So the value is 8, and the correct option is (d).

Simple interest Formula: $SI=\frac{P\times R\times T}{100}$ Here SI=576, R=6 and T=3. $576=\frac{P\times 6\times 3}{100}=\frac{18P}{100}$ $P=\frac{576\times 100}{18}=3200$ So the principal is ₹3,200 - option (c).

Successive profit and loss Let Ketan's cost price be x. Ketan sells at 5% profit, so Mahesh pays $x\times \frac{105}{100}=1.05x$. Mahesh sells at 24% loss, so David pays $1.05x\times \frac{76}{100}=0.798x$. David actually paid ₹3990, so 0.798x=3990. $x=\frac{3990}{0.798}=5000$ Ketan's cost price was ₹5,000 - option (c).

Population growth A 25% yearly rise multiplies the population by $\frac{5}{4}$ each year. So to go back one year, multiply by $\frac{4}{5}$. 1 year ago $=110000\times \frac{4}{5}=88000$ 2 years ago $=88000\times \frac{4}{5}=70400$ 3 years ago $=70400\times \frac{4}{5}=56320$ Required difference =70400-56320=14080 - option (c).

Inverse proportion Inversely proportional means $x\propto \frac{1}{y}$, i.e. one grows exactly as fast as the other shrinks. Replacing the proportionality sign by a constant k gives $x=\frac{k}{y}$. Cross-multiplying, xy=k - the product stays constant. Option (a) $\frac{x}{y}=k$ is the test for direct proportion, so it is not the answer. Hence the correct option is (d).

Speed, time and delay For a fixed distance, time is inversely proportional to speed. Speed becomes $\frac{3}{4}$, so time becomes $\frac{4}{3}$ of the normal time. Let the normal time be T: extra time $=\frac{4}{3}T-T=\frac{T}{3}$. $\frac{T}{3}=24\Rightarrow T=72$ The normal journey takes 72 minutes - option (c).

Price, consumption, expenditure Expenditure = price × consumption, so fix easy numbers: price =100, consumption =100, expenditure =10000. Price rises by 50%, so the new price is 150. Expenditure is allowed to rise by 11% only: new expenditure $=10000\times \frac{111}{100}=11100$. New consumption $=\frac{11100}{150}=74$ Fall in consumption =100-74=26 out of 100, i.e. 26% - option (b). Note that 74% is the consumption that remains, not the cut, which is why (d) is the trap here.

Average of weights Turn every average into a total: total = average $\times$ number of people. $S+R+M=46\times 3=138$ $S+R=39\times 2=78$, so M=138-78=60. $R+M=48\times 2=96$, so R=96-60=36. Rupesh weighs 36 kg - option (a).

Successive discounts For two successive discounts a and b, the single equivalent discount is $a+b-\frac{ab}{100}$. Here a=18.5 and b=11.5. $=18.5+11.5-\frac{18.5\times 11.5}{100}$ $=30-\frac{212.75}{100}=30-2.1275$ =27.8725 The single equivalent discount is 27.8725% - option (c). Simply adding the two discounts gives 30%, which is why (a) is wrong.

Cost price from gain A gain of 8.5% is always measured on the cost price, so $SP=CP\times \frac{108.5}{100}$. $217=CP\times \frac{108.5}{100}$ $CP=\frac{217\times 100}{108.5}$ CP=200 The article cost ₹200 - option (d).

Nested brackets, BODMAS Start with the innermost bracket: 16-12=4. So $\frac{16-12}{4}=\frac{4}{4}=1$. Curly bracket next: $7÷7\times 1=1\times 1=1$. Round bracket: $19\times 8=152$. Whole expression $=152\times 1=152$ - option (c).

Percentage of a number "4% of x" means $\frac{4}{100}\times x$. $\frac{4x}{100}=48$ 4x=4800 x=1200 So x=1200 - option (d).

Nested brackets, BODMAS Open the brackets from the inside out. Innermost round bracket: 6-5=1. Curly bracket: $16-2\times 1\times 8=16-16=0$. Square bracket: $2+5\times 0÷31=2+0=2$. Finally $50-7\times 2=50-14=36$. So the value is 36 - option (a). Because the curly bracket is exactly 0, the $÷31$ never changes anything.

BODMAS order BODMAS: division and multiplication come before addition and subtraction. $12÷4=3$ and $3\times 4=12$. $16+12÷4-3\times 4=16+3-12$ =19-12=7 So the value is 7 - option (c).

Average of consecutive numbers For an odd count of consecutive numbers the average is exactly the middle term. With 19 terms the middle one is the 10th, so the 10th number is 41. The 1st term is 9 steps before the 10th. Smallest =41-9=32 So the smallest number is 32 - option (b).

CI and SI difference Simple interest for 2 years is ₹42, so one year's interest is $\frac{42}{2}=21$. For 2 years, CI - SI =43-42=1; this ₹1 is only the interest earned on the first year's interest of ₹21. $21\times \frac{R}{100}=1\Rightarrow R=\frac{100}{21}$ per cent per annum. $P=\frac{SI\times 100}{R\times T}=\frac{42\times 100}{\frac{100}{21}\times 2}$ $=\frac{4200\times 21}{200}=441$ The principal is ₹441 - option (a).

Time and work Take the total work as the LCM of 16, 12 and 4, i.e. 48 units. A does $\frac{48}{16}=3$ units a day; B does $\frac{48}{12}=4$ units a day. All three together do $\frac{48}{4}=12$ units a day. C alone does 12-(3+4)=5 units a day. Days needed by C $=\frac{48}{5}$ - option (b).

Ratio, income and saving Income : expenditure =6:5, and the 5 parts of expenditure are ₹4,50,000. One part $=\frac{450000}{5}=90000$, so income $=6\times 90000=540000$. New income $=540000\times \frac{140}{100}=756000$ New expenditure $=450000\times \frac{80}{100}=360000$ Final saving =756000-360000=396000, i.e. ₹3,96,000 - option (a).

Hemisphere surface area Plating is done on the inside only, so the area needed is the curved surface of a hemisphere, $2\pi r^2$ (the flat rim disc and the outside are not plated). $2\pi r^2=2\times \frac{22}{7}\times 3.5\times 3.5$ $=2\times 22\times 0.5\times 3.5=77$, so the area is 77 sq cm. Cost $=77\times 4=308$ The tin plating costs ₹308 - option (a).

Average speed both ways The two legs cover the same distance, so the average speed is the harmonic mean, not the ordinary mean. Formula: average speed $=\frac{2xy}{x+y}$ $=\frac{2\times 4\times 12}{4+12}=\frac{96}{16}$ =6 The average speed is 6 km/hr - option (b). The ordinary average $\frac{4+12}{2}=8$ is wrong because far more time is spent on the slow leg.