Question
The number of pencils with ‘Ravi’ and ‘Shyam’ together is 30 more than that with ‘Karan’, while the number of pencils with ‘Shyam’ and ‘Karan’ together is 20 more than that with ‘Ravi’. If ‘Ravi’ and ‘Karan’ together have a total of 70 pencils, then find the number of pencils with ‘Ravi’, ‘Shyam’, and ‘Karan’, together.
Solution
Let the number of pencils with ‘Ravi’, ‘Shyam’, and ‘Karan’ be ‘x’, ‘y’, and ‘z’, respectively. Therefore, x+y=z+30 ………(1) y+z=x+20 ………(2) x+z=70 ………(3) Add equations (1), (2), and (3): 2(x+y+z)=x+z+120 Or, 2(x+y+z)=70+120 Or, x+y+z=190/2=95 Thus, the total number of pencils with Ravi, Shyam, and Karan together is 95.
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