Traffic Optimization Problem

Question 66: Traffic Congestion Problem

• Four cars go from Akala (A) to Bakala (B) via Mamur (M) or Nanur (N).
• A to M and N to B each take 6 minutes for one car.
• Each extra car adds 3 minutes per car due to congestion on A to M, and N to B.
• A to N takes 20 minutes for one car, with each extra car adding 1 minute per car.
• M to B takes 20 minutes for one car, with each extra car adding 0.9 minute per car.
• The police mandates particular routes to each car to prevent cars from gaining travel time by not following the order while others do
• A new one-way road from M to N is available.
• A to B has three possible routes: A-M-B, A-N-B, and A-M-N-B.
• M to N takes 7 minutes for one car, with each extra car adding 1 minute per car.
• Cars taking the A-M-N-B route travel A-M at the same time as those taking A-M-B.
• Cars taking the A-M-N-B route travel N-B at the same time as those taking A-N-B.
• The objective is to find the minimum travel time from A to B if all cars follow the orders.
• The police will not order all cars to use the same route.

Question 67: Age Calculation Problem

• Arun's current age is 40% of Barun's age.
• In a few years, Arun's age will be half of Barun's age.
• The problem asks for the percentage increase in Barun's age during this period.

Question 68: Work Completion Problem

• A person does a job in 120 days working alone.
• On each subsequent day, a new person joins the work, each with same efficiency.
• The problem asks to find the number of days needed to finish the job.

Question 69: Elevator Capacity Problem

• An elevator has a weight limit of 630 kg.
• The elevator is carrying a group of people whose heaviest member weighs 57 kg and the lightest weighs 53 kg.
• The problem asks to find the maximum possible number of people in the group.

Question 70: Speed and Distance Problem

• A man walking at 12 kmph reaches a railway station 10 minutes after the train's departure.
• Walking at 15 kmph, he reaches the station 10 minutes before the train's departure.
• The problem asks to find the distance from his home to the railway station.

Question 71: Savings and Investments Problem

• Ravi invests 50% of his monthly savings in fixed deposits.
• 30% of the remaining savings goes to stocks, and the rest to a savings bank account.
• The total amount deposited in the bank (savings account and fixed deposits) is Rs 59500.
• The problem asks to find Ravi's total monthly savings.

Question 72: Retail and Discount Problem

• A seller gives a 15% discount on the retail price but still makes a 2% profit.
• The question asks which scenario ensures a 20% profit.

Question 73: Motorboat and River Problem

• Man travels by motor boat down a river to his office and back.
• Doubling the speed of the motor boat reduces his total travel time by 75%.
• The problem asks to find the ratio of the original speed of the motor boat to the speed of the river.

Question 74: Profit Ratio Problem

• Five companies C1, C2, C3, C4, and C5 are given.
• Profit ratio of C1:C2:C3 is 9:10:8.
• Profit ratio of C2:C4:C5 is 18:19:20.
• C5's profit is Rs 19 crore more than C1's.
• The objective is to find total profit made by all the five companies.

Question 75: Admission Test Problem

• Number of girls appearing for an admission test is twice the number of boys.
• 30% of the girls and 45% of the boys get admission.
• The problem asks for the percentage of candidates who do not get admission.

Question 76: Ratio and Proportion problem

• Sold popcorn and chips in packets of three sizes: large, super, and jumbo.
• The number of large, super, and jumbo packets in stock are in the ratio 7:17:16 for popcorn and 6:15:14 for chips.
• The total number of popcorn packets is equal to chips packets.
• Find the number of jumbo popcorn packets and number of jumbo chips packets in the ratio

Question 77: Profit Percentage problem

• Medium quality mangoes is half that of good mangoes.
• Shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market.
• Sells all these at a common price with is 10% less that at which he bought the good ones.
• Find overall profit

Question 78: Percentage Discount problem

• Fatima sells 60 equivalent toys at a 40% discount on the printed tag price making 20% profit on initial value.
• Ten of these toys are destroyed in a fire.
• How much discount should be given so that she can make the same amount of profit?

Question 79: Integers Proportion problem

• Find the ratio a: b
• a and b are integers of opposite signs such that (a + 3)² : b² = 9 : 1 and (a - 1)² : (b - 1)² = 4 : 1.

Question 80: Average Score Problem

• Class consists of 20 boys and 30 girls.
• In the mid-semester examination, the average score of the girls was 5 higher than that of the boys.
• In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2.
• The increase in the average score of the boys is

Question 81: Area Measurement Problem

• Closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane.
• find the area of the closed region

Question 82: Area under Curve Problem

• Triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft,
• Triangular portion GBC is cut off where G is the centroid of ABC.
• Find The area, in sq ft, of the remaining portion of triangle ABC

Question 83: Arc Length Problem

• Triangle ABC be a right-angled isosceles triangle with hypotenuse BC.
• BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC.
• If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC

Question 84: Surface Area comparison Problem

• A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1: 1: 8:27:27.
• The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube

Question 85: Vertical Measurement Problem

• A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically.
• The height of the cylinder is 3 cm, while its volume is 9 π cm³.
• The vertical distance, in cm, of the topmost point of the ball from the base of the cylinder

Question 86: Time required Problem

• Triangle ABC be a right-angled triangle with BC as the hypotenuse.
• Lengths of AB and AC are 15 km and 20 krn, respectively.
• The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour

Question 87: Lograthmic Problem

• Suppose, log3 x = log12 y = a, where x, y are positive numbers.
• If G is the geometric mean of x and y, and log6 G

Question 88: Algebric Problem

• If x + 1 = x² and x > 0, then 2x⁴ is

Question 89: Lograthmic values Problem

• find the value of log0.008 √5 + log √3 81-7 5

Question 90: Algebric exponents Problem

• If 9²ˣ ⁻ ¹ – 81ˣ⁻¹ = 1944, then x is

Question 91: Algebraic equation Problem

• The number of solutions to the equation x - y - z = 25.
• x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12

Question 92: Inequalities Problem

• For how many integers n, will the inequality (n − 5) (n – 10) – 3(n − 2) ≤ 0 be satisfied?

Question 93: Functions Problem

• Defined f₁(x) = x² + 11x + n and f2(x) = x.
• Find The largest positive integer n for which the equation f₁(x) = f2 (x) has two distinct real roots,

Question 94: Whole Numbers Problem

• If a, b, c, and d are integers such that a + b + c + d = 30,
• find The minimum possible value of (a - b)² + (a - c)² + (a - d)²

Question 95: Triangles with circle Problem

• AB, CD, EF, GH, and JK be five diameters of a circle with center at O.
• In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

Question 96: Curve distance Problem

• Find The shortest distance of the point ( , ) from the curve y = |x -1| + |x + 1|
• 2
• 3

Question 97: Arthimetic Progression Problem

• If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms,
• Find the ration of the first term to the common difference

Question 98: Distribution Problem

• In how many ways can 7 identical erasers be distributed among 4 kids
• each kid gets at least one eraser but nobody gets more than 3 erasers?

Question 99: Function values Problem

• If f(x) = 5x+2 and g(x) = x²-2x – 1,
• 3x 3.
• find the value of g(f((3)))

Question 100: Arithmetic Problem

• Let a1, a2,........a3n be an arithmetic progression with a₁ = 3 and a2 = 7.
• If a₁ + a2 + ....+a3n = 1830, then what is the smallest positive integer m such that m(a₁ + a2 + + an) > 1830?