In a 2- hour examination of 100 questions, there are 30 grammar questions. If half as much time should be allowed for each grammar questions as for each of the other questions, how many minutes should be spent on all the grammar questions?

Solution

Let x [if gte msEquation 12]>x [if !msEquation]--> [endif]-->be the time allowed per regular question, `x/2` [if gte msEquation 12]> x 2 [if !msEquation]--> [endif]-->is the time allowed per grammar question. [if gte msEquation 12]>∴ [if !msEquation]--> [endif]-->Total time for all the regular questions = 70 [if gte msEquation 12]>x [if !msEquation]--> ^x and Total time for all the grammar question = 30(`x/2` ) = 15x [if gte msEquation 12]>x [if !msEquation]--> [endif]--> [if gte msEquation 12]>∴ [if !msEquation]--> [endif]-->70 x + 15x [if gte msEquation 12]> x [if !msEquation]--> [endif]-->= 120 minutes, 85x [if gte msEquation 12]> x [if !msEquation]--> [endif]-->= 120, and [if gte msEquation 12]>x [if !msEquation]--> [endif]-->x = `120/85` [if gte msEquation 12]> 120 85 [if !msEquation]--> [endif]-->= [if gte msEquation 12]> 24 17 [if !msEquation]--> [endif]-->.`24/17` [if gte msEquation 12]>∴ [if !msEquation]--> [endif]-->The time to do a grammar question is (`24/(17xx2)` [if gte msEquation 12]> 24 17 ×   2 [if !msEquation]--> [endif]-->) = [if gte msEquation 12]> 12 17 [if !msEquation]--> [endif]-->.`12/17` [if gte msEquation 12]>∴ [if !msEquation]--> [endif]-->Total time to do all the grammar questions = 30`xx12/17` [if gte msEquation 12]>× 12 17 [if !msEquation]--> [endif]-->= `360/17` [if gte msEquation 12]> 3 17 [if !msEquation]--> [endif]-->minutes.