Question

Solve for x and y : √2 x + √3 y = 5 and √3 x − √8 y = −√6

Assertion (A) : The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1. Reason (R) : If the pair of linear equations px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique solution, then p ≠ 1.

A telecommunication company came up with two plans– plan A and plan B for its customers. The plans are represented by linear equations where 't' represents the time (in minutes) bought and 'C' represents the cost. The equations are : Plan A : 3C = 20t Plan B : 3C = 10t + 300 Based on above information, answer the following questions :

The monthly income of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in ratio 5:7. If each saves ₹ 15,000 per month, find their monthly incomes.