Aptitude: Arithmetic and Numerical Ability

• These study notes cover arithmetical and numerical ability questions.

Question 1

• If x = √17+ √93 - √17 - √93, then the value of x lies between 2 and 2.5

Question 2

• The ratio of mangoes to apples is 3:7
• After removing 4 mangoes and 4 apples, the ratio becomes 2:5.
• Initially, there were 120 mangoes and apples in total.

Question 3

• Simple interest on a sum for 12 years at 7.5% p.a. is ₹1,225 less than the amount of the same sum for 22 years at 6% p.a.
• The sum is ₹4,900.

Question 4

• Pipe A fills a tank in 12 hours, and pipe B fills it in 15 hours.
• Pipe C empties the tank.
• When all pipes are open, 15% of the tank is filled in 6 hours.
• Pipe C alone can empty 5/16 of the tank in 3 3/4 hours.

Question 5

• The price of an item increased successively by 35% and 15%, then decreased by 40% and 10%
• The final price is ₹1,676.70
• The initial price was ₹2,000.

Question 6

• A is 20% less efficient than B.
• B completes work in 40 days
• C completes the same work in 60 days.
• A and B work together for 10 days.
• A and C complete the remaining work in 15 days.

Question 7

• Let 'x' be the greatest number which when divided by 1982, 3738 and 6811, the remainder in each case is 'y'.
• The value of (3x - 5y) is 183

Question 8

• The marked price of an article is ₹550.
• It is sold for ₹425.92 after two successive discounts of x% each.
• Sold by giving a single discount of 2x%, its selling price will be ₹418.

Question 9

• Solution A contains liquids 11, 12, and 13 in the ratio 3:4:8
• Solution B contains liquids 11 and 12 in the ratio 7:8
• Solution C contains liquids 12 and 13 in the ratio 3:7
• Two litres of A, 3 litres of B and 5 litres of C are mixed.
• The percentage of 12 in the new solution is 36 2/3 %

Question 10

• A grassy triangular field has sides of 95 m, 168 m, and 193 m.
• A horse is tethered at each corner with a 42 m rope
• The area of the field left ungrazed is 5190 m².

Question 11

• Sujatha's monthly expenditure is ₹35,280, which is 16% less than her monthly income.
• Her monthly income increases by 15% and monthly expenditure by 25%.
• Her monthly savings are ₹4,200.

Question 12

• A sphere of maximum volume is carved from a wooden cube of side 24 cm.
• The sphere's volume equals a solid cylinder of height 36 cm
• the cylinder's curved surface area is 576π cm².

Question 13

• A and B start a business with capitals in the ratio 5/12 : 1/6.
• After 4 months, A increases his capital by one-third, and B doubles his capital.
• After one year, B's share in a total profit of ₹42.5 lakhs is ₹18 lakhs.

Question 14

• A trader sells sarees for ₹1,260 each after a 25% discount
• Without the discount, he would have earned 40% profit.
• The cost price of each saree is ₹1,200

Question 15

• When x is subtracted from 29, 45, 38, and 62, the numbers are in proportion.
• The mean proportional between (2x+5) and (x-7) is 3√6.

Question 16

• A man travels 100 km at 50 km/h, 120 km at 40 km/h, and 150 km at 60 km/h.
• The average speed for the whole journey is 48 8/31 km/h.

Question 17

• Graph shows annual tea production in states A and B from 2017-2020 (in million kg).
• In 2021, state A's tea production increased by the same percentage as in 2020 over 2019.
• State B's tea production increased by 20% over 2020.
• The total tea production by states A and B in 2021 exceeds 2020 by 270 million kg.

Question 18

• Train A and B speeds are 64 km/h and 71 km/h respectively, running opposite on parallel tracks.
• Train B is 230 m long.
• If they cross each other in 16 seconds, train A is 470 m long.

Question 19

• Rekha invested savings in schemes A and B in a 5:9 ratio for 1 1/2 years.
• Scheme A offers 20% p.a. compounded half-yearly, Scheme B at compounded yearly,
• The total interest is ₹13,605, the sum invested in Scheme A is ₹16,000.

Question 20

• Selling an article at 67.5% of its selling price causes a 19% loss.

• Selling at 90% of its original price yields profit

• The profit percent is 8%