Direct Questions CAT 2024 Quant Slot 1

The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

Suppose \( x_1, x_2, x_3, \ldots, x_{100} \) are in an arithmetic progression such that \( x_5 = -4 \) and \( 2x_6 + 2x_9 = x_{11} + x_{13} \). Then, \( x_{100} \) equals

If the equations \( x^2 + mx + 9 = 0 \), \( x^2 + nx + 17 = 0 \), and \( x^2 + (m + n)x + 35 = 0 \) have a common negative root, then the value of \( (2m + 3n) \) is

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work fordouble the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is