5 February 2025 · Shift 2

Compound interest ratio Let Vijay receive V and Ajay receive A, so that V+A=1617. Both amounts are equal, so $V{\left(1+\frac{10}{100}\right)}^{15}=A{\left(1+\frac{10}{100}\right)}^{16}$ $\frac{V}{A}={\left(1+\frac{10}{100}\right)}^{16-15}=\frac{11}{10}$ So V:A=11:10 and the total is 11+10=21 parts. 21 parts $=1617\Rightarrow 1$ part $=\frac{1617}{21}=77$ Vijay's share $=11\times 77=847$ Therefore Mahesh gave Vijay ₹847, so the correct option is (a).

Average with a new member Total age of the 30 students $=30\times 18=540$ years With the teacher the group has 31 members and the average becomes 18+1=19 years. New total age $=31\times 19=589$ years Teacher's age =589-540=49 years Shortcut: teacher's age = new average + (number of students $\times$ rise) $=19+30\times 1=49$ Therefore the correct option is (a).

Profit by false weight Suppose the shopkeeper claims to sell 1000 g of goods. The weight is $21\%$ less, so he actually hands over 1000-210=790 g. He charges the cost of 1000 g but parts with goods that cost him only 790 g. Profit $\%=\frac{\mathrm{claimed}\mathrm{weight}-\mathrm{actual}\mathrm{weight}}{\mathrm{actual}\mathrm{weight}}\times 100$ $=\frac{1000-790}{790}\times 100=\frac{210\times 100}{790}=\frac{2100}{79}$ $\frac{2100}{79}=26\frac{46}{79}$, because $26\times 79=2054$ and 2100-2054=46. Therefore the profit is $26\frac{46}{79}\%$, so the correct option is (b).

Time when two trains meet Between 9:00 A.M. and 10:00 A.M. only the first train is moving. Distance it covers $=20\times 1=20$ km Distance still between them at 10:00 A.M. =370-20=350 km They now move towards each other, so relative speed =20+50=70 km/hr Time to meet $=\frac{350}{70}=5$ hours Meeting time = 10:00 A.M. +5 hours = 3:00 P.M. Therefore the correct option is (a).

LCM and HCF relation For any two numbers, $\mathrm{LCM}\times \mathrm{HCF}=\mathrm{first}\mathrm{number}\times \mathrm{second}\mathrm{number}$ $168\times 6=24\times x$ 1008=24x $x=\frac{1008}{24}=42$ Check: $\mathrm{HCF}\left(24,42\right)=6$ and $\mathrm{LCM}\left(24,42\right)=168$, as required. Therefore the other number is 42, so the correct option is (b).

BODMAS simplification By BODMAS, solve the innermost bracket first: 7-2=5 $\frac{21}{5}\times 5=21$ Now the braces: $\frac{48}{8}+21=6+21=27$ The first bracket: $44÷4=11$ Finally $11\times 27=297$ Therefore the correct option is (d).

Literacy percentage Number of females =369000-186000=183000 Total literates $=45\%$ of $369000=\frac{45}{100}\times 369000=166050$ Literate males $=45\%$ of $186000=\frac{45}{100}\times 186000=83700$ Literate females =166050-83700=82350 Required percentage $=\frac{82350}{183000}\times 100=45\%$ Therefore the correct option is (c).

Volume of a cuboid Volume of a cuboid $V=l\times b\times h$ New length =2l, new breadth =3b, new height $=\frac{h}{2}$ New volume $=2l\times 3b\times \frac{h}{2}$ $=\frac{2\times 3}{2}\times lbh=3lbh$ So the new volume =3V. Therefore the correct option is (d).

Average of three weights Anwar + Amit + Gopal $=3\times 45=135$ kg Anwar + Amit $=2\times 43=86$ kg Amit + Gopal $=2\times 42=84$ kg Adding the last two lines: Anwar $+2\times$ Amit + Gopal =86+84=170 kg Subtracting the first line: Amit =170-135=35 kg Therefore the correct option is (a).

BODMAS evaluation By BODMAS, division and multiplication are done first, from left to right. $32÷8=4$ $4\times 3=12$ and $3\times 3=9$ The expression becomes 12-9=3 Therefore the correct option is (d).

Difference of simple interest Simple interest $=\frac{P\times R\times T}{100}$ Both sums run at the same rate for the same time, so the difference of interest comes only from the difference of principals. Difference of principals =9400-5400=4000 $\frac{4000\times R\times 6}{100}=960$ 240R=960 $R=\frac{960}{240}=4$ Therefore the rate is $4\%$ per annum, so the correct option is (c).

Successive percentage change Take the original price as 100. After a rise of $15\%$: $100\times \frac{115}{100}=115$ After a fall of $12\%$: $115\times \frac{88}{100}=101.2$ After a rise of $8\%$: $101.2\times \frac{108}{100}=109.296$ Net change =109.296-100=9.296 So the price rises by about $9.3\%$, correct to one decimal place. Therefore the correct option is (b).

BODMAS simplification Innermost bracket first: 8-2=6 $\frac{17}{6}\times 6=17$ Now the braces: $\frac{64}{4}+17=16+17=33$ The first bracket: $91÷7=13$ Finally $13\times 33=429$ Therefore the correct option is (d).

Trains crossing in same direction To cross completely, the faster train must cover the sum of the two lengths. Distance =170+480=650 m They run in the same direction, so relative speed =80-70=10 km/h 10 km/h $=10\times \frac{5}{18}=\frac{25}{9}$ m/s Time $=\frac{650}{\frac{25}{9}}=650\times \frac{9}{25}=234$ s Time in minutes $=\frac{234}{60}=3.9$ Therefore the correct option is (d).

Work on alternate days B begins, so B works on days 1, 3, 5, 7, 9, 11 and A works on days 2, 4, 6, 8, 10. The work ends in the middle of day 12, which is A's day, so A also works half of that day. In $11\frac{1}{2}$ days B works 6 days and A works $5\frac{1}{2}$ days. A alone needs 22 days, so A's one day work $=\frac{1}{22}$ Work done by A $=\frac{11}{2}\times \frac{1}{22}=\frac{1}{4}$ Work done by B $=1-\frac{1}{4}=\frac{3}{4}$, and B took 6 days for it. B's one day work $=\frac{3}{4}÷6=\frac{1}{8}$, so B alone finishes the whole work in 8 days. Time for B to do $\frac{3}{4}$ of the work $=\frac{3}{4}\times 8=6$ days Therefore the correct option is (c).

Division in a given ratio Let the shares be 4x, 8x and 3x. 4x+8x+3x=4800 15x=4800 $x=\frac{4800}{15}=320$ Shyam's share $=8x=8\times 320=2560$ Therefore Shyam receives ₹2,560, so the correct option is (d).

Fourth proportional If a:b::c:d, then the fourth proportional is $d=\frac{b\times c}{a}$. $F_1=\frac{\frac{7}{12}\times 8}{\frac{2}{7}}=\frac{14}{3}\times \frac{7}{2}=\frac{49}{3}$ $F_2=\frac{\frac{4}{3}\times 10}{\frac{5}{6}}=\frac{40}{3}\times \frac{6}{5}=16$ $F_1:F_2=\frac{49}{3}:16$ Multiplying both parts by 3: $F_1:F_2=49:48$ Therefore the correct option is (b).

Compound interest ratio Let Anand receive x and Anil receive y, so that x+y=1612. Both amounts are equal, so $x{\left(1+\frac{8}{100}\right)}^{13}=y{\left(1+\frac{8}{100}\right)}^{14}$ $\frac{x}{y}={\left(1+\frac{8}{100}\right)}^{14-13}=\frac{108}{100}=\frac{27}{25}$ So x:y=27:25 and the total is 27+25=52 parts. 52 parts $=1612\Rightarrow 1$ part $=\frac{1612}{52}=31$ Anand's share $=27\times 31=837$ Therefore Manoj gave Anand ₹837, so the correct option is (d).

Selling price from profit percent $\mathrm{SP}=\mathrm{CP}\times \left(1+\frac{\mathrm{Profit}}{100}\right)$ $=500\times \left(1+\frac{28}{100}\right)$ $=500\times \frac{128}{100}$ =640 Therefore he should sell it for ₹640, so the correct option is (c).

Markup with discount Let the cost price be 100. Marked price $=100+20\%$ of 100=120 Selling price $=120-20\%$ of 120=120-24=96 Since 96<100, there is a loss of 100-96=4 Loss $\%=\frac{4}{100}\times 100=4\%$ Therefore the correct option is (a).