A market research group conducted a survey of 1000 consumers and reported that 720 consumers liked product A and 450 consumers liked product B. What is the least number that must have liked both products?

A market research group conducted a survey of 500 consumers and reported that 400 consumers liked product A and 300 consumers liked product B. What is the least number that must have liked both products

A company studies the product preferences of 300 consumers. It was found that 226 liked product A, 51 liked product B, 54 liked product C,21 liked products A and B , 54 liked products A and C, 39 liked products B and C and 9 liked all the three products. Prove that, the study results are not correct. [ Assume that each consumer likes at least one of the three products.]

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

A toy company manufacturers two types of dolls, A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company make profit of Rs. 12 ad Rs. 16 doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?

One mole of glycerol is treated with an excess of HIO_4 . The number of moles of HIO_4 consumed and the product are respectively

After watching a programme on TV about the presence of caricinogens (cancer causing agents) potassium bromate and potassium iodate in bread and other bakery products, Ritu a class XII student decided to aware others about the adverse effects of these carcinogens in foods, She consulted the school principal and requested him to instruct the canteen contractor to stop selling sandwiches, pizzas, burgers, and other bakery products to the students. The principal took an immediate action and insturcted the canteen contractor to replace the bakery product with some proteins and vitamins rich food like fruits, salads, sprouts etc. The decision was welcomed by the parents and students. What are the values (at least two) displayed by Ritu?

After watching a programme on TV about the presence of caricinogens (cancer causing agents) potassium bromate and potassium iodate in bread and other bakery products, Rupali a class XII student decided to aware others about the adverse effects of these carcinogens in foods, She consulted the school principal and requested him to instruct the canteen contractor to stop selling sandwiches, pizzas, burgers, and other bakery products to the students. The principal took an immediate action and insturcted the canteen contractor to replace the bakery product with some proteins and vitamins rich food like fruits, salads, sprouts etc. The decision was welcomed by the parents and students. What are the values (at least two) displayed by Rupali?

Represent the following situations with suitable mathematical equations. Sridhar and Rajendar together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles now they have is 124. We would like to find out how many marbles each of them had previously.