Question 1

If 12 books cost ₹480, what is the cost of 18 books?

Accepted Answer

Step 1: Cost of 1 book = 480 ÷ 12 = ₹40. Step 2: Cost of 18 books = 18 × 40 = ₹720.

Question 2

The ratio of boys to girls in a class is 5:3. If there are 40 boys in the class, how many girls are there?

Accepted Answer

Step 1: Let the number of boys = 5x and girls = 3x. Step 2: Given 5x = 40, so x = 8. Step 3: Number of girls = 3x = 3 × 8 = 24.

Question 3

A sum of money is divided among P, Q, and R in the ratio 2 : 3 : 5. If R receives ₹1000, what is the total sum?

Accepted Answer

Step 1: P : Q : R = 2 : 3 : 5. Step 2: Let the shares be 2x, 3x, and 5x respectively. Step 3: R's share = 5x = 1000. Step 4: Therefore x = 200. Step 5: Total sum = 2x + 3x + 5x = 10x = 10 × 200 = ₹2000.

Question 4

The ratio of ages of Amit and Bhavna is 5:7. If Amit is 20 years old, what is Bhavna's age?

Accepted Answer

Step 1: Let Amit's age = 5x and Bhavna's age = 7x (from ratio 5:7). Step 2: Given Amit is 20 years old, so 5x = 20, which gives x = 4. Step 3: Bhavna's age = 7x = 7 × 4 = 28 years.

Question 5

The ratio of two numbers is 3:5. If each number is increased by 10, the new ratio becomes 5:7. What is the smaller of the two original numbers?

Accepted Answer

Step 1: Let the two numbers be 3x and 5x. Step 2: After adding 10 to each: (3x + 10)/(5x + 10) = 5/7. Step 3: Cross multiply: 7(3x + 10) = 5(5x + 10) → 21x + 70 = 25x + 50 → 4x = 20 → x = 5. Step 4: The two numbers are 3×5 = 15 and 5×5 = 25. Therefore, the smaller number is 15.

Question 6

The ratio of ages of A and B is 5:7. If A is 15 years old, what is B's age?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x (from ratio 5:7). Step 2: Given A = 15, so 5x = 15, which gives x = 3. Step 3: B's age = 7x = 7 × 3 = 21 years.

Question 7

The ratio of ages of A and B is 3 : 4. If A is 18 years old, how old is B?

Accepted Answer

Step 1: A : B = 3 : 4. Step 2: A's age = 18 years. Step 3: Let A's age = 3x and B's age = 4x. Step 4: 3x = 18, so x = 6. Step 5: B's age = 4x = 4 × 6 = 24 years.

Question 8

If A : B = 3 : 5 and B : C = 2 : 3, find A : B : C.

Accepted Answer

Step 1: A : B = 3 : 5 means A/B = 3/5. Step 2: B : C = 2 : 3 means B/C = 2/3. Step 3: To combine, make B the same in both ratios. LCM(5, 2) = 10. Step 4: A : B = 3 : 5 = 6 : 10 (multiply by 2). Step 5: B : C = 2 : 3 = 10 : 15 (multiply by 5). Step 6: Therefore A : B : C = 6 : 10 : 15.

Question 9

A sum of ₹1200 is divided among three people in the ratio 2:3:5. How much does the person with the largest share receive?

Accepted Answer

Step 1: Total parts = 2 + 3 + 5 = 10. Step 2: Value of 1 part = ₹1200 ÷ 10 = ₹120. Step 3: Largest share corresponds to 5 parts = 5 × ₹120 = ₹600.

Question 10

Two numbers are in the ratio 7:4. If their difference is 45, what is the larger number?

Accepted Answer

Step 1: Let the numbers be 7x and 4x. Step 2: Their difference = 7x − 4x = 3x = 45. Step 3: x = 15. Step 4: Larger number = 7x = 7 × 15 = 105.

Question 11

If A:B = 3:5 and B:C = 2:3, what is A:B:C?

Accepted Answer

Step 1: A:B = 3:5 means A = 3k, B = 5k for some constant k. Step 2: B:C = 2:3 means B = 2m, C = 3m for some constant m. Step 3: Since B is common, 5k = 2m, so m = 5k/2. Step 4: C = 3m = 3 × (5k/2) = 15k/2. Step 5: To avoid fractions, multiply all by 2: A:B:C = 6:10:15.

Question 12

The ratio of two numbers is 4 : 7. If their difference is 45, find the larger number.

Accepted Answer

Step 1: Let the two numbers be 4x and 7x. Step 2: Their difference is 7x − 4x = 3x. Step 3: Given that 3x = 45, so x = 15. Step 4: The larger number is 7x = 7 × 15 = 105.

Question 13

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is the sum of their ages?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x (from ratio 5:7). Step 2: Given A is 15 years younger than B, so 7x - 5x = 15, which gives 2x = 15, thus x = 7.5. Step 3: A's age = 5(7.5) = 37.5 years, B's age = 7(7.5) = 52.5 years. Step 4: Sum = 37.5 + 52.5 = 90 years.

Question 14

The ratio of boys to girls in a class is 4:5. If there are 12 more girls than boys, how many students are there in total?

Accepted Answer

Step 1: Let boys = 4x and girls = 5x (from ratio 4:5). Step 2: Given girls are 12 more than boys, so 5x - 4x = 12, which gives x = 12. Step 3: Boys = 4(12) = 48, Girls = 5(12) = 60. Step 4: Total students = 48 + 60 = 108.

Question 15

The ratio of boys to girls in a class is 7:5. If there are 84 boys, what is the total number of students in the class?

Accepted Answer

Step 1: Boys:Girls = 7:5. Step 2: Let boys = 7x and girls = 5x. Step 3: Given boys = 84, so 7x = 84, therefore x = 12. Step 4: Girls = 5x = 5 × 12 = 60. Step 5: Total students = 84 + 60 = 144.

Question 16

A recipe requires flour and sugar in the ratio 5:2. If 350 grams of flour is used, how much sugar (in grams) is needed?

Accepted Answer

Step 1: Flour:Sugar = 5:2. Step 2: Let flour = 5x and sugar = 2x. Step 3: Given flour = 350 grams, so 5x = 350, therefore x = 70. Step 4: Sugar = 2x = 2 × 70 = 140 grams.

Question 17

A mixture contains milk and water in the ratio 3:2. If the mixture contains 15 litres of milk, how many litres of water are in the mixture?

Accepted Answer

Step 1: Milk:Water = 3:2. Step 2: Let milk = 3x and water = 2x. Step 3: Given milk = 15 litres, so 3x = 15, therefore x = 5. Step 4: Water = 2x = 2 × 5 = 10 litres.

Question 18

If x:y = 4:5 and y:z = 2:3, what is x:z?

Accepted Answer

Step 1: x:y = 4:5 means x/y = 4/5. Step 2: y:z = 2:3 means y/z = 2/3. Step 3: To find x:z, we need x/z = (x/y) × (y/z) = (4/5) × (2/3) = 8/15. Step 4: Therefore x:z = 8:15.

Question 19

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is A's current age?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x (from ratio 5:7). Step 2: Given A is 15 years younger than B, so 7x - 5x = 15. Step 3: 2x = 15, therefore x = 7.5. Step 4: A's age = 5x = 5 × 7.5 = 37.5 years.

Question 20

The ratio of two numbers is 3:5. If 6 is added to each number, the ratio becomes 2:3. What is the smaller of the two numbers?

Accepted Answer

Step 1: Let the two numbers be 3x and 5x. Step 2: After adding 6 to each: (3x + 6)/(5x + 6) = 2/3. Step 3: Cross-multiply: 3(3x + 6) = 2(5x + 6) → 9x + 18 = 10x + 12 → x = 6. Step 4: The two numbers are 3×6 = 18 and 5×6 = 30. The smaller number is 18.

Question 21

If x:y = 3:5 and y:z = 2:3, what is x:y:z?

Accepted Answer

Step 1: x:y = 3:5 means x/y = 3/5. Step 2: y:z = 2:3 means y/z = 2/3. Step 3: To combine ratios, make y the same in both. In x:y, y = 5 (coefficient). In y:z, y = 2 (coefficient). Step 4: LCM(5, 2) = 10. Step 5: Multiply x:y = 3:5 by 2 to get x:y = 6:10. Step 6: Multiply y:z = 2:3 by 5 to get y:z = 10:15. Step 7: Now y is 10 in both, so x:y:z = 6:10:15.

Question 22

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹480, what is the total sum of money?

Accepted Answer

Step 1: Let the shares be 5x, 7x, and 8x respectively. Step 2: Difference between B and A = 7x - 5x = 2x = ₹480. Step 3: Solving, x = 240. Step 4: Total sum = 5x + 7x + 8x = 20x = 20 × 240 = ₹4800.

Question 23

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹480, then what is the total sum of money divided?

Accepted Answer

Step 1: Let the shares of A, B, and C be 5x, 7x, and 8x respectively. Step 2: The difference between B's and A's shares is 7x - 5x = 2x. Step 3: Given that 2x = 480, so x = 240. Step 4: Total sum = 5x + 7x + 8x = 20x = 20 × 240 = ₹4,800.

Question 24

A profit of ₹1200 is divided among three partners in the ratio 2:3:5. The difference between the largest and smallest share is:

Accepted Answer

Step 1: Let shares be 2x, 3x, and 5x. Step 2: Total = 2x + 3x + 5x = 10x = 1200. Step 3: Solving, x = 120. Step 4: Largest share = 5x = 5(120) = 600. Step 5: Smallest share = 2x = 2(120) = 240. Step 6: Difference = 600 - 240 = 360.

Question 25

The ratio of ages of two persons P and Q is 4:5. After 8 years, the ratio of their ages will be 6:7. What is the sum of their present ages?

Accepted Answer

Step 1: Let present ages be 4x and 5x. Step 2: After 8 years, ages are (4x+8) and (5x+8). Step 3: Set up equation: (4x+8)/(5x+8) = 6/7. Step 4: Cross-multiply: 7(4x+8) = 6(5x+8). Step 5: 28x + 56 = 30x + 48. Step 6: -2x = -8, so x = 4. Step 7: Present ages are 16 and 20. Sum = 36.

Question 26

Three containers have milk in the ratio 3:4:5. If 10 litres is transferred from the third container to the first, the new ratio becomes 5:4:3. What was the original quantity of milk in the second container?

Accepted Answer

Step 1: Let original quantities be 3x, 4x, and 5x litres. Step 2: After transfer, quantities are (3x+10), 4x, and (5x-10). Step 3: New ratio is 5:4:3, so (3x+10):(4x):(5x-10) = 5:4:3. Step 4: From first and second: (3x+10)/4x = 5/4 → 4(3x+10) = 5(4x) → 12x+40 = 20x → x = 5. Step 5: Original quantity in second container = 4x = 4(5) = 20 litres.

Question 27

A mixture contains milk and water in the ratio 5:3. If 16 litres of water is added, the ratio becomes 5:7. How many litres of milk are in the original mixture?

Accepted Answer

Step 1: Let milk and water be 5x and 3x litres. Step 2: After adding 16 litres of water: 5x:(3x+16) = 5:7. Step 3: Cross-multiply: 7(5x) = 5(3x+16). Step 4: 35x = 15x + 80 → 20x = 80 → x = 4. Step 5: Milk = 5x = 5(4) = 20 litres.

Question 28

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹480, then what is the total sum of money divided?

Accepted Answer

Step 1: Let the shares of A, B, and C be 5x, 7x, and 8x respectively. Step 2: The difference between B's and A's shares is 7x - 5x = 2x. Step 3: Given that 2x = 480, so x = 240. Step 4: Total sum = 5x + 7x + 8x = 20x = 20 × 240 = ₹4,800.

Question 29

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹600, what is the total sum of money?

Accepted Answer

Step 1: Let the shares be 5x, 7x, and 8x respectively. Step 2: Difference between B and A = 7x - 5x = 2x = 600. Step 3: Solving, x = 300. Step 4: Total sum = 5x + 7x + 8x = 20x = 20(300) = ₹6000.

Question 30

Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. Find the larger number.

Accepted Answer

Step 1: Let the numbers be 3x and 5x. Step 2: After increasing by 10: (3x+10):(5x+10) = 5:7. Step 3: Cross-multiply: 7(3x+10) = 5(5x+10). Step 4: 21x + 70 = 25x + 50 → 20 = 4x → x = 5. Step 5: Larger number = 5x = 5(5) = 25.

Question 31

In a mixture, the ratio of milk to water is 7:3. If 20 litres of water is added to the mixture, the ratio becomes 7:5. How many litres of milk were in the original mixture?

Accepted Answer

Step 1: Let original quantities be 7x litres of milk and 3x litres of water. Step 2: After adding 20 litres of water, milk remains 7x and water becomes (3x+20). Step 3: New ratio is 7:5, so 7x/(3x+20) = 7/5. Step 4: Cross-multiply: 5(7x) = 7(3x+20) → 35x = 21x + 140 → 14x = 140 → x = 10. Step 5: Original milk = 7x = 7(10) = 70 litres.

Question 32

Three containers have liquids in the ratio 2:3:4. If the second container has 15 litres more than the first, what is the total quantity of liquid in all three containers?

Accepted Answer

Step 1: Let quantities be 2x, 3x, and 4x litres. Step 2: Difference between second and first = 3x - 2x = x = 15. Step 3: Solving, x = 15. Step 4: Total = 2x + 3x + 4x = 9x = 9(15) = 135 litres.

Question 33

The ratio of ages of father and son is 7:3. After 10 years, the ratio will be 9:5. What is the father's current age?

Accepted Answer

Step 1: Let current ages be 7x and 3x. Step 2: After 10 years: (7x+10):(3x+10) = 9:5. Step 3: Cross-multiply: 5(7x+10) = 9(3x+10). Step 4: 35x + 50 = 27x + 90 → 8x = 40 → x = 5. Step 5: Father's age = 7x = 7(5) = 35 years.

Question 34

If A:B = 7:5 and B:C = 5:4, then A:B:C is equal to:

Accepted Answer

Step 1: A:B = 7:5 means A = 7k and B = 5k for some constant k. Step 2: B:C = 5:4 means B = 5m and C = 4m for some constant m. Step 3: Since B is common, 5k = 5m, so k = m. Step 4: Therefore A:B:C = 7k:5k:4k = 7:5:4.

Question 35

A sum of ₹1200 is divided between Raj and Priya in the ratio 3:5. How much does Priya receive?

Accepted Answer

Step 1: Total parts = 3 + 5 = 8. Step 2: Priya's share = (5/8) × 1200. Step 3: Priya's share = 5 × 150 = ₹750.

Question 36

If A : B = 3 : 5 and B : C = 2 : 3, then find A : B : C.

Accepted Answer

Step 1: A : B = 3 : 5 means A/B = 3/5. Step 2: B : C = 2 : 3 means B/C = 2/3. Step 3: To combine, make B the same in both ratios. LCM(5, 2) = 10. Step 4: A : B = 3 : 5 = 6 : 10 (multiply by 2). Step 5: B : C = 2 : 3 = 10 : 15 (multiply by 5). Step 6: Therefore A : B : C = 6 : 10 : 15.

Question 37

The ratio of boys to girls in a class is 5:3. If there are 40 boys in the class, how many girls are there?

Accepted Answer

Step 1: Let the common factor be x. Then boys = 5x and girls = 3x. Step 2: Given boys = 40, so 5x = 40, which gives x = 8. Step 3: Number of girls = 3x = 3 × 8 = 24.

Question 38

The ratio of ages of Amit and Bhavna is 5:7. If Amit's age is 25 years, what is Bhavna's age?

Accepted Answer

Step 1: Given ratio of ages = Amit : Bhavna = 5 : 7. Step 2: Amit's age = 25 years. Step 3: Let Amit's age = 5x and Bhavna's age = 7x. Step 4: Since 5x = 25, we get x = 5. Step 5: Therefore, Bhavna's age = 7x = 7 × 5 = 35 years.

Question 39

The ratio of boys to girls in a class is 4 : 5. If there are 20 boys, how many girls are there?

Accepted Answer

Step 1: Boys : Girls = 4 : 5. Step 2: Let boys = 4x and girls = 5x. Step 3: Given boys = 20, so 4x = 20. Step 4: x = 5. Step 5: Girls = 5x = 5 × 5 = 25.

Question 40

A sum of ₹1200 is divided between A and B in the ratio 2 : 3. How much does B receive?

Accepted Answer

Step 1: A : B = 2 : 3. Step 2: Total parts = 2 + 3 = 5. Step 3: B's share = (3/5) × 1200. Step 4: B's share = 3 × 240 = 720.

Question 41

If 4 pens cost ₹60, how much will 10 pens cost?

Accepted Answer

Step 1: Cost of 1 pen = 60 ÷ 4 = ₹15. Step 2: Cost of 10 pens = 15 × 10 = ₹150.

Question 42

If x : 8 = 6 : 4, then the value of x is:

Accepted Answer

Step 1: x : 8 = 6 : 4. Step 2: Using the property of proportion, x/8 = 6/4. Step 3: Cross multiply: 4x = 8 × 6. Step 4: 4x = 48. Step 5: x = 12.

Question 43

Two numbers are in the ratio 7 : 9. If their difference is 8, find the larger number.

Accepted Answer

Step 1: Let the two numbers be 7k and 9k. Step 2: Difference = 9k - 7k = 2k. Step 3: Given difference = 8, so 2k = 8. Step 4: k = 4. Step 5: Larger number = 9k = 9 × 4 = 36.

Question 44

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is A's current age?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x (from ratio 5:7). Step 2: Given A is 15 years younger than B, so 7x - 5x = 15. Step 3: 2x = 15, therefore x = 7.5. Step 4: A's age = 5x = 5 × 7.5 = 37.5 years.

Question 45

If A:B = 3:4 and B:C = 5:6, then A:B:C is equal to:

Accepted Answer

Step 1: A:B = 3:4 means A/B = 3/4. Step 2: B:C = 5:6 means B/C = 5/6. Step 3: To combine, find LCM of B values (4 and 5) = 20. Step 4: Rewrite A:B = 3:4 as 15:20 (multiply by 5). Step 5: Rewrite B:C = 5:6 as 20:24 (multiply by 4). Step 6: Therefore A:B:C = 15:20:24.

Question 46

A sum of money is divided among P, Q, and R in the ratio 3:5:7. If R receives ₹2100 more than P, what is the total sum?

Accepted Answer

Step 1: Let P's share = 3x, Q's share = 5x, and R's share = 7x. Step 2: Given R receives ₹2100 more than P, so 7x - 3x = 2100, which gives 4x = 2100, thus x = 525. Step 3: Total sum = 3x + 5x + 7x = 15x = 15(525) = ₹7875.

Question 47

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is the sum of their ages?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x. Step 2: Given that A is 15 years younger than B, so 7x - 5x = 15, which gives 2x = 15, thus x = 7.5. Step 3: A's age = 5(7.5) = 37.5 years and B's age = 7(7.5) = 52.5 years. Step 4: Sum = 37.5 + 52.5 = 90 years.

Question 48

A certain amount is divided among X, Y, and Z in the ratio 1:2:3. If Z receives ₹300 more than X, what is Y's share?

Accepted Answer

Step 1: Let X's share = 1k, Y's share = 2k, Z's share = 3k. Step 2: Z receives ₹300 more than X, so 3k - 1k = 300. Step 3: 2k = 300, therefore k = 150. Step 4: Y's share = 2k = 2(150) = ₹300.

Question 49

In a mixture, the ratio of milk to water is 7:3. If 20 litres of water is added, the ratio becomes 7:5. How many litres of milk are in the original mixture?

Accepted Answer

Step 1: Let original milk = 7x and original water = 3x. Step 2: After adding 20 litres of water, milk = 7x and water = 3x + 20. Step 3: New ratio is 7:5, so 7x/(3x+20) = 7/5. Step 4: Cross multiply: 5(7x) = 7(3x+20). Step 5: 35x = 21x + 140. Step 6: 14x = 140, so x = 10. Step 7: Original milk = 7x = 7(10) = 70 litres.

Question 50

The ratio of present ages of two brothers is 4:5. After 8 years, the ratio will be 6:7. What is the sum of their present ages?

Accepted Answer

Step 1: Let present ages be 4x and 5x. Step 2: After 8 years, ages will be (4x+8) and (5x+8). Step 3: New ratio is 6:7, so (4x+8)/(5x+8) = 6/7. Step 4: Cross multiply: 7(4x+8) = 6(5x+8). Step 5: 28x + 56 = 30x + 48. Step 6: -2x = -8, so x = 4. Step 7: Present ages are 4(4) = 16 and 5(4) = 20. Step 8: Sum = 16 + 20 = 36 years.

Question 51

Two numbers are in the ratio 4:9. If their difference is 35, what is the larger number?

Accepted Answer

Step 1: Let the two numbers be 4x and 9x. Step 2: Their difference is 9x - 4x = 5x = 35, so x = 7. Step 3: The larger number = 9x = 9(7) = 63.

Question 52

The ratio of boys to girls in a school is 7:5. If there are 840 more boys than girls, how many girls are there in the school?

Accepted Answer

Step 1: Let the number of boys = 7x and the number of girls = 5x. Step 2: Given that there are 840 more boys than girls, so 7x - 5x = 840, which gives 2x = 840, thus x = 420. Step 3: Number of girls = 5x = 5(420) = 2100.

Question 53

The ratio of boys to girls in a school is 5:7. If there are 480 more girls than boys, how many boys are there in the school?

Accepted Answer

Step 1: Let boys = 5x and girls = 7x. Step 2: Difference = 7x - 5x = 2x = 480. Step 3: x = 240. Step 4: Number of boys = 5 × 240 = 1200.

UP Police SI Basic Ratio & Proportion

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