Question 1

Divide ₹4,500 into two parts in the ratio 2 : 3.

Accepted Answer

Let the two parts be 2x and 3x. Then, 2x + 3x = 4500 => 5x = 4500 => x = 900. So, the two parts are 2*900 = ₹1800 and 3*900 = ₹2700. — The sum of the parts is ₹4500. The ratio is 2:3, so total parts = 2+3=5. Each part is 4500/5 = 900. Multiply 900 by 2 and 3 to get the two amounts.

Question 2

In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain?

Accepted Answer

Total parts = 1 + 5 = 6. Volume of acid = (1/6) × 240 = 40 mL. Volume of water = (5/6) × 240 = 200 mL. — The total solution is 240 mL. The ratio of acid to water is 1:5, so total parts = 6. Divide 240 mL into 6 parts, each part is 40 mL. Acid is 1 part = 40 mL, water is 5 parts = 200 mL.

Question 3

Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of these two colours are needed? To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint?

Accepted Answer

Total parts = 3 + 5 = 8. Blue paint = (3/8) × 40 = 15 mL. Yellow paint = (5/8) × 40 = 25 mL. After adding 20 mL yellow, new yellow = 25 + 20 = 45 mL. Blue remains 15 mL. New ratio = 15 : 45 = 1 : 3. — First, divide 40 mL into 8 parts. Blue is 3 parts, yellow is 5 parts. Then add 20 mL yellow to the original 25 mL yellow. The blue quantity remains the same. Simplify the new ratio.

Question 4

To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need?

Accepted Answer

Total parts = 2 + 1 = 3. Rice = (2/3) × 6 = 4 cups. Urad dal = (1/3) × 6 = 2 cups. — The total mixture is 6 cups. The ratio is 2:1, so total parts = 3. Divide 6 cups into 3 parts, each part is 2 cups. Rice is 2 parts = 4 cups, urad dal is 1 part = 2 cups.

Question 5

I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. I added another bucket of yellow paint to this mixture. What is the ratio of red paint to yellow paint in the new mixture?

Accepted Answer

Let the volume of one bucket be x. Red paint = (3/8) x, Yellow paint = (5/8) x. Added another bucket of yellow paint = x. Total yellow paint = (5/8) x + x = (13/8) x. Ratio of red to yellow = (3/8) x : (13/8) x = 3 : 13. — Original mixture has red and yellow in 3:5 ratio, total parts 8. One bucket volume is x. Red paint is 3/8 x, yellow is 5/8 x. Adding one more bucket of yellow paint adds x volume. Total yellow is 5/8 x + x = 13/8 x. Ratio red:yellow = 3:13.

Question 6

Anagh mixes 600 mL of orange juice with 900 mL of apple juice to make a fruit drink. Write the ratio of orange juice to apple juice in its simplest form.

Accepted Answer

Ratio = 600 mL : 900 mL = 600/300 : 900/300 = 2 : 3. — Divide both quantities by their greatest common divisor, which is 300, to simplify the ratio.

Question 7

Last year, we hired 3 buses for the school trip. We had a total of 162 students and teachers who went on that trip and all the buses were full. This year we have 204 students. How many buses will we need? Will all the buses be full?

Accepted Answer

Last year: 3 buses for 162 people => 162/3 = 54 people per bus. This year: 204 students. Number of buses needed = 204/54 = 3.78, so 4 buses are needed. Since 4 buses can carry 4 × 54 = 216 people, all buses will not be full. — Calculate capacity per bus from last year. Divide this year's students by capacity to find number of buses. Since 204 is less than 216, buses won't be full.

Question 8

The area of Delhi is 1,484 sq. km and the area of Mumbai is 550 sq. km. The population of Delhi is approximately 30 million and that of Mumbai is 20 million people. Which city is more crowded? Why do you say so?

Accepted Answer

Population density of Delhi = 30,000,000 / 1,484 ≈ 20,211 people per sq. km. Population density of Mumbai = 20,000,000 / 550 ≈ 36,364 people per sq. km. Mumbai is more crowded because it has a higher population density. — Calculate population density by dividing population by area for both cities. Compare the densities to determine which is more crowded.

Question 9

A crane of height 155 cm has its neck and the rest of its body in the ratio 4 : 6. For your height, if your neck and the rest of the body also had this ratio, how tall would your neck be?

Accepted Answer

Total parts = 4 + 6 = 10. Neck length = (4/10) × 155 cm = 62 cm. For your height h, neck length = (4/10) × h = 0.4h. — Divide the total height into 10 parts according to the ratio. Neck is 4 parts, so multiply total height by 4/10 to get neck length.

Question 10

Let us try an ancient problem from Lilavati. At that time weights were measured in a unit named palas and niskas was a unit of money. “If 2 palas of saffron costs niskas, O expert businessman! tell me quickly what quantity of saffron can be bought for 9 niskas?”

Accepted Answer

Given: 2 palas cost 3 niskas. Cost per pala = 3/2 niskas. For 9 niskas, quantity = 9 ÷ (3/2) = 9 × (2/3) = 6 palas. — Find cost per pala by dividing total cost by quantity. Then divide 9 niskas by cost per pala to find quantity.

Question 11

Divide ₹4,500 into two parts in the ratio 2 : 3.

Accepted Answer

Let the two parts be 2x and 3x. Then, 2x + 3x = 4500 => 5x = 4500 => x = 900. So, the two parts are 2x = 1800 and 3x = 2700. — The sum of parts is 4500. Since ratio is 2:3, total parts = 2+3=5. Each part = 4500/5=900. Multiply by ratio terms to get parts.

Question 12

In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain?

Accepted Answer

Total parts = 1 + 5 = 6. Volume of acid = (1/6) × 240 = 40 mL. Volume of water = (5/6) × 240 = 200 mL. — The total solution is divided into 6 parts according to the ratio. Acid is 1 part, water is 5 parts. Multiply total volume by ratio fractions.

Question 13

Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of these two colours are needed? To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint?

Accepted Answer

Total parts = 3 + 5 = 8. Blue paint = (3/8) × 40 = 15 mL. Yellow paint = (5/8) × 40 = 25 mL. After adding 20 mL yellow, yellow = 25 + 20 = 45 mL. New ratio = blue : yellow = 15 : 45 = 1 : 3. — First find amounts of blue and yellow in 40 mL using ratio. Then add 20 mL yellow and simplify the new ratio.

Question 14

To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need?

Accepted Answer

Total parts = 2 + 1 = 3. Rice = (2/3) × 6 = 4 cups. Urad dal = (1/3) × 6 = 2 cups. — Divide total mixture into 3 parts according to ratio. Multiply total quantity by ratio fractions to get individual quantities.

Question 15

I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. I added another bucket of yellow paint to this mixture. What is the ratio of red paint to yellow paint in the new mixture?

Accepted Answer

Let the volume of one bucket be x. Initially, red paint = (3/8)x, yellow paint = (5/8)x. Added yellow paint = x. Total yellow paint = (5/8)x + x = (13/8)x. New ratio red : yellow = (3/8)x : (13/8)x = 3 : 13. — Calculate initial amounts using ratio and bucket volume. Add one bucket of yellow paint. Simplify the new ratio.

PROPORTIONAL 7 REASONING-1

PROPORTIONAL 7 REASONING-1 — Study Notes

Introduction to Proportional Reasoning

Equivalent Ratios

Proportion and Its Properties

Practice Questions — PROPORTIONAL 7 REASONING-1

All 7 Chapters in Ganita Prakash Part-I