General Mathematics & Basic Arithmetic — Part 1 MCQs with Explanations

Present ratio is 5:4 so let present ages be 5x and 4x. After 3 years ratio is 11:9 so (5x+3) / (4x+3) = 11/9 9(5x+3) = 11(4x+3) 45x+27 = 44x+33 45x-44x = 33-27 x = 6 Adnan present age = 4x = 4*6 = 24 years

Convert the speeds of the trains from km/h to m/s 1 km/h = 1000 m/3600 s Speed of the first train = 60 km/h = (60,000 m/3600 s) m/s = 16.67 m/s. Speed of the second train = 45 km/h = (45,000 m/3600 s) m/s = 12.50 m/s. Relative speed = Speed of the first train - Speed of the second train = 16.67 m/s - 12.50 m/s = 4.17 m/s. Distance = Length of the second train = 500 meters. Using the formula: Distance = Speed × Time Time = Distance / Relative speed = 500 meters / 4.17 m/s = 120.05 seconds. To convert the time from seconds to minutes, we divide by 60: Time in minutes = 120.05 seconds / 60 = 2 minutes (approximately). Therefore, the first train will cross the second train after approximately 2 minutes.

Second winner arrived at 9:55. Race started at 9:00. Time taken by second = 9:55 - 9:00 = 55 minutes Second took 10 minutes more than first, so: First = 55 - 10 = 45 minutes

He reached on Thursday and was 3 days early. So scheduled day = Thursday + 3 days = Sunday Now "coming Monday" is 4 days after Thursday. Thursday -> Friday -> Saturday -> Sunday -> Monday[scheduled] So Monday is 1 day AFTER Sunday. He would be 1 day late.

1. A can give B 15 points in 60 It means when A makes 60 points, B makes only 60 - 15 = 45 points. So, Ratio A : B = 60 : 45 2. A can give C 20 points in 60 It means when A makes 60 points, C makes only 60 - 20 = 40 points. So, Ratio A : C = 60 : 40 3. Find B : C Make A equal in both. When A = 60, B = 45 and C = 40 So when B = 45, C = 40 When B = 90, C = (40 / 45) x 90 = 80 So in a game of 90, when B makes 90, C makes only 80. B can give C = 90 - 80 = 10 points in a game of 90.

When two dice are rolled, there are 36 possible outcomes The outcomes that result in a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), which are 6 in total. So, the probability of getting a sum of 7 is 6/36 = 1/6.

Calculate the cube root of 32768. ³√32768 = ³√32³ = 32

17% of 51 = (17/100) × 51 = 8.67

S I = 100 P × R × T ​ S I = 2000 × 10 × 3/ 100 ​ = 600 ​

Total ratio = 2+3=5 2 + 3 = 5 Largest part = 3/5 ​ × 500 = 300 ​

(x²+x−20)/(x²−4) Step 1: Factorize the numerator and denominator. x²+ x − 20 = ( x + 5 ) ( x − 4 ) x²− 4 = ( x − 2 ) ( x + 2 ) Step 2: Write the simplified expression. (x+5)(x−4)​/(x−2)(x+2) ​

Let the number be x . According to the question: 3 x − 54 = 36 Add 54 to both sides: 3 x = 36 + 54 = 90 Divide by 3: x = 90/3 ​ = 30 ​

Number = 600 × 100/3 ​ = 20 , 000

Check the relation between terms: 2 x 2 = 4 4 x 2 = 8 8 x 2 = 16 Each term is multiplied by 2 to get the next term. Next term = 16 x 2 = 32

Decrease in temperature = Day temperature − Midnight temperature 2 0 ∘ C − 1 6 ∘ C = 4 ∘ C

Odd Positions: 3, 4, 6 Pattern: +1, +2 Even Positions: 4, 5, 6 Pattern: +1, +1 The missing number is in the 6th position, which belongs to the even-position series. Calculation: ( 5 + 1 = 6 )

We are given: log₅ 125 = x We know that: 125 = 5³ So, log₅ 125 = log₅ (5³) = 3

A circle has no straight sides or vertices . A triangle has 3 sides, while a square and a diamond (rhombus) have 4 straight sides each. Therefore, the circle does not belong to the group because it is the only shape without straight sides .

Given: 1. D is at the extreme right. So position 4 is D. _ , _ , _ , D 2. A is to the left of B. So A comes before B. 3. C is to the right of B. So C comes after B. Combine 2 and 3: A comes, then B, then C. So A, B, C. Put them in the line with D at the end: Position 1 = A Position 2 = B Position 3 = C Position 4 = D So second from the left is B.

3 x 2 = 6 6 x 2 = 12 12 x 2 = 24 24 x 2 = 48

Total Distance = 300 + 300 = 600 km Total Time = 4 + 6 = 10 hours Average Speed = Total Distance / Total Time = 600 / 10 = 60 km/h

Book is created by Author . Painting is created by Artist .

Distance from starting point = 3 km. He goes 5 km North then 5 km South = back to same horizontal line. So only 3 km East remains.

Pattern is -10 each time: 100 - 10 = 90 90 - 10 = 80 80 - 10 = 70 70 - 10 = 60 60 - 10 = 50

Sara is older than Ayesha, so Sara > Ayesha. Sara is younger than Fatima, so Fatima > Sara. Therefore, the age order is Fatima > Sara > Ayesha, making Fatima the eldest .

Each letter is shifted one step forward in the alphabet. T → U, E → F, A → B, C → D, H → I, E → F, R → S. Applying the same rule: C → D, H → I, A → B, I → J, R → S. Correct code: CHAIR → DIBJS

Average = (2 + 4 + 6 + x) / 4 = 3 12 + x = 12 x = 0

Required fraction = 45 / 120 = 15 _ 3 / 15 _ 8 = 3/8

Total ratio parts = 4 + 3 + 2 = 9 1 part = 1800 / 9 = 200 votes Ms. Frau = 3 parts = 3 * 200 = 600

Convert to decimal: 1/2 = 0.5 3/5 = 0.6 2/3 = 0.66 3/4 = 0.75 Small to big = 0.5 < 0.6 < 0.66 < 0.75 So = 1/2, 3/5, 2/3, 3/4

Total spent = 40% + 25% + 15% = 80% Remaining = 100% - 80% = 20%

5 machines = 5 widgets in 5 minutes So 1 machine = 1 widget in 5 minutes 100 machines will make 100 widgets in same 5 minutes (each machine makes 1)

Let A's present age = x 10 years ago: Mother's age = 4 _ (x - 10) After 10 years: Mother's age = 2 _ (x + 10) Difference between those two mother ages is 20 years: 4(x - 10) + 20 = 2(x + 10) 4x - 40 + 20 = 2x + 20 4x - 20 = 2x + 20 2x = 40 x = 20 years

3x + 1 = x 3x - x = -1 2x = -1 x = -1/2

If x = -3, then x^2 + 3x + 3 = (-3)^2 + 3*(-3) + 3 = 9 - 9 + 3 = 3

Total distance to cover = Train length + Platform length = 150 + 250 = 400 m Speed = 60 km/hr = 60 × 5/18 = 50/3 m/sec Time = Distance / Speed = 400 / (50/3) = 400 × 3 / 50 = 24 seconds

Total parts = 5 + 9 = 14 parts 14 parts = 5,600 tons 1 part = 5,600 / 14 = 400 tons Larger ship = 9 parts = 9 × 400 = 3,600 tons

Let first = A, second = B 2/5 of A = 1/3 of B A × 2/5 = B × 1/3 A/B = (1/3) / (2/5) A/B = 1/3 × 5/2 = 5/6 So ratio A : B = 5 : 6

(1/3 + 2/3) / 2 = (1) / 2 = 1/2

The negative numbers and positive numbers balance each other. -10 - 40 = -50 20 + 30 = 50 -50 and +50 makes 0, so average is 0 .