3 (c) 14.5 hours 25. Mini and Vinay are quiz masters preparing for a quiz. In x minutes, Mini makes y questions more than Vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in x minutes Mini would make 2y questions more than Vinay. How many questions does Mini make in x minutes? 2 (a) 1/4[2(x + y) - V(2x2 + 4y2)] (b) 1/4[2(x - y) - 1(2x + 4y2)] (c) Either a orb (d) 1/4 [2(x – y) - V(2x2 - 4y2)] D D - b
Answers
Answer:
Let Mini and Vinay take M and V minutes to frame a question respectively.
Mini takes M mins to frame 1 question.
Therefore Mini takes x mins to frame xM questions.
Vinay takes V mins to frame 1 question.
Therefore Vinay takes x mins to frame xV questions.
ATQ:
xM=xV+y(1)
Multiplying the above equation by 2 yields:
2xM=2xV+2y(1a)
Now, in the second scenario:
Mini takes (M-2) mins to frame 1 question.
Therefore Mini takes x mins to frame x(M−2) questions.
Vinay takes V-2 mins to frame 1 question.
Therefore Vinay takes x mins to frame x(V−2) questions.
Therefore ATQ:
xM−2=xV−2+2y(2)
Equating 2y from (1)a and 2 yields:
xM−2−xV−2=2xM−2xV
1M−2−1V−2=2M−2V
V−2−M+2(M−2)(V−2)=2V−2MMV
V−MMV−2M−2V+4=2V−2MMV
(V−M)MV=2(V−M)(MV−2M−2V+4)
MV=2MV−4M−4V+8
MV−4M−4V+8=0
Step-by-step explanation: