Which of the following vary directly and which vary inversely with each other and which are neither of the two?
(i) The quantity of rice and its cost.
(ii) The height of a tree and the number of years.
(iii) Increase in cost and number of shirts that can be purchased if the budget remains the same.
(iv) Area of land and its cost.
(v) Sales Tax and the amount of the bill
Solution:
(i) The quantity of rice and its cost are directly related to each other. As one buys more quantities of rice the cost of buying it will increase.It is a direct variation.
(ii) The height of the tree and the number of years are not related to each other either directly or inversely. There are many trees which do not grow beyond a certain height and trees do not grow infinitely. They stop growing after a certain time as in the case of humans.
(iii) Increase in the cost and number of shirts that can be purchased if the budget remains same are inversely related to each other. If the budget remains same then as the cost per shirt increases the number of shirts that can be bought by budgeted amount will be less. This is an inverse variation.
(iv) Area of the land and its cost are directly related. The larger the area of the land the larger the cost given that that cost per unit area remains constant.
(v) Sales Tax and the amount of bill are directly related to each other. Higher the bill amount higher will be the sales tax calculated on the bill amount.
✦ Try This: Which of the following vary directly and which vary inversely with each other and which are neither of the two? (i) The procurement price of rice is Rs. 2500 per quintal. How will 4 quintals of rice cost? If 8 quintals are purchased what will be the total cost?
Purchase price of rice = Rs. 2500/quintal
Therefore,
Cost of Purchasing 4 quintals of Rice = Rs. 2500 × 4 = Rs. 10,000
Cost of purchasing 8 quintals of Rice = Rs.2500 × 8 = Rs. 20,000
Hene the cost of purchasing rice is dependent on the quantity of rice purchased as the rate of procurement is constant i.e. Rs. 2500 per quintal.
(ii) Ram goes shopping to buy shirts for himself. His budget is Rs. 2000. How many shirts can he buy if the price per shirt is a) Rs. 400 and b) Rs. 250?
a) Price of each shirt = Rs.400
Number of shirts that can be purchased by Ram = 2000/400 = 5 shirts
b) Price per shirt = Rs. 250
Number of shirts that can be purchased by Ram = 2000/250 = 8 shirts
Hence with a fixed budget the number of shirts bought are inversely proportional to the price of the shirt.
(iii) Land is available for sale @ Rs. 5000 per sq. metre. What will be the cost of the land of 100 sq metre area? If the area available for sale is 150 sq. metre then what will be its cost?
Land is priced at Rs. 5000 per sqm.
Therefore the cost of 100 sqm of land will be = Rs. 5000 × 100 = Rs. 5,00,000
The cost of 150 sqm of land will cost = Rs. 5000 × 150 = Rs. 7,50,000
Hence the area of the land and the cost of land are directly proportional.
(iv) The sales tax at a shopping mall is charged flatly @5% on the bill amount. Sheila goes to the mall shopping on Monday and Friday and on both days her shopping bill at the billing counter of the Mall was Rs. 4000 and Rs. 6000 respectively. What is the sales tax on the two bill amounts?
Sales Tax rate = 5% on the bill amount
(a) Amount of sales tax on bill of Rs. 4000 = 5% × 4000 = (5/100) × 4000 = Rs. 200
(b) Amount of sales tax on bill of Rs. 5000 = 5% × 5000 = (5/1000 × 5000 = rs. 250
Hence we see that the sales tax amount is directly proportional to the bill amount.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13
NCERT Exemplar Class 8 Maths Chapter 10 Problem 62
Which of the following vary directly and which vary inversely with each other and which are neither of the two?(i) The quantity of rice and its cost (ii) The height of a tree and the number of years (iii) Increase in cost and number of shirts that can be purchased if the budget remains the same (iv) Area of land and its cost (v) Sales Tax and the amount of the bill
Summary:
(i) The quantity of rice and its cost are directly related to each other.
(ii) The height of the tree and the number of years are not related to each other either directly or inversely.
(iii) Increase in the cost and number of shirts that can be purchased if the budget remains same are inversely related to each other.
(iv) Area of the land and its cost are directly related.
(v) Sales Tax and the amount of bill are directly related to each other.
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