Question

(a) If ſ part of a pole is inside the mud, ſ part is inside the water, and the remaining length of 10 m is above the surface of the water, find the length of the pole.

(b) Bishwant had some money. He spent ſ part of his money to buy goods for his birthday, 5 parts of the money he gave to his sister, and the rest of Rs 40 he gave to his mother. How much money did he have at first?

(c) If ſ part of the distance between two places is 45 km, find the distance between the places.

(d) If ſ part of the total number of students of a school are girls, and there are 240 boys, find the number of girls.

(e) Divide Rs 350 in the ratio of 4:3.

(f) A man divides Rs 7200 between his son and daughter in the ratio of 4:5. Find the shares of each of them.

(g) Ram, Hari, and Shyam invest a sum of Rs 15000 on a business in the ratio of...

Answer 1

Scale models and ratio problems in mathematics involve converting actual measurements to scaled measurements and dividing quantities based on specified ratios. Using scale factors like 1/36 or 1/72 can determine model sizes, while ratios can help distribute money or other goods.

Step-by-step explanation:

Scale Models and Ratio Problems

Students often encounter questions related to scale models, ratio, and proportional reasoning in mathematics. These problems require understanding how to convert measurements based on a given scale factor and how to divide quantities based on a specified ratio. For example, if the actual length of a boat is 24 feet and the scale factor is 1/36, the model should be 8 inches long since there are 12 inches in a foot, so (24 feet * 12 inches/foot) / 36 = 8 inches. With a scale factor of 1/72, the model would be 4 inches long.

In another scenario, dividing Rs 350 in the ratio of 4:3 would give Rs 200 and Rs 150, respectively. When dividing Rs 7200 in a ratio of 4:5, the shares would be Rs 2880 for the son and Rs 4320 for the daughter. In the scale drawing context, a metal pipe that is 2.5 meters long drawn using a scale factor of 1/100 would be 2.5 cm in the drawing because 2.5 meters is 250 cm, and 250 cm / 100 = 2.5 cm.