Fractions
Fractions is an concept from the MPSC syllabus, tested in 4 past MPSC questions across 4 exam years between 2015 and 2023. Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
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मेजवानीसाठी जमलेल्या कुटुंबियांनी दोघात मिळून एक भाताचे भांडे, तिघात मिळून एक डाळीचे भांडे, पाचात मिळून एक भाजीचे भांडे आणि सहा जणांन मिळून एक श्रीखंडाचे भांडे, याप्रमाणे एकूण 108 भांडी पदार्थ मागवले. यामुळे कोणताही पदार्थ जास्त झाला वा कमी पडला नाही तर एकूण किती कुटुंबिय मेजवानीला उपस्थित होते ? Relatives who had gathered for a party had one bowl of rice between two, one bowl of dal among three, one bowl of vegetable among five and one bowl of shreekhand among six. In all they ordered 108 bowls of eatables; and no food was wasted or was it short. How many relatives were present for the party ?
Let total relatives be x. Bowls equation: x/2 + x/3 + x/5 + x/6 = 108. Taking LCM (30), (15x + 10x + 6x + 5x)/30 = 108 => 36x/30 = 108 => x = 90.
सर्व विद्यार्थ्यांच्या गटात 2/5 मुली आहेत आणि यातील 2/3 मुलींनी गणितात 90% च्या वर गुण मिळवले. जर 36 मुलींनी गणितात 90% च्या वर गुण मिळवले असतील तर मुली नसलेल्या विद्यार्थ्यांची संख्या दर्शवणारा पर्याय निवडा.
Let total students = x. Girls = (2/5)x. Girls with >90% = (2/3)*(2/5)x = (4/15)x = 36. Solving gives x = 135. Non-girls (boys) = x - (2/5)x = (3/5)x = (3/5)*135 = 81.
मिना, जीवा व फारू यांनी काही रक्कम वाटून घेतली. मिनािला 5/8 मिळाली, जीवाला 0.25 आणि फारूला 75 रुपये मिळाले. मूळ रक्कम दर्शविणारा पर्याय निवडा. Mina, Jiva and Faru share out a certain sum of money between them. Mina receives 5/8, Jiva receives 0.25 and Faru receives Rs. 75. Select options that indicates the original amount.
Let total amount be x. Mina gets 5/8 x, Jiva gets 0.25x (which is 1/4 x or 2/8 x). Remaining for Faru = x - (5/8 + 2/8)x = 1/8 x = 75. Therefore, total amount x = 75 * 8 = 600.
S जवळ काही रंगीबेरंगी शिंपले आहेत. यातील एक तृतीयांश शिवाय 14 जादा शिंपले तिने P ला दिले. P ने यातील एक तृतीयांश शिवाय 11 जादा शिंपले Q ला दिले. Q ने यातील एक तृतीयांश शिवाय एक जादा शिंपला तिच्या R या मित्राला दिला. जर R ला Q कडून 14 शिंपले मिळाले तर S कडे मुळात असलेल्या शिंपल्यांची संख्या निवडा. S is having some colourful sea shells. She gave one third of these shells and 14 more besides to P. P gave one third of these shells and 11 more besides to Q. Q gave one third of these shells and one more besides to her friend R. If R got 14 shells from Q then select the number of shells S originally has.
Working backwards from R: R got 14 shells. Q gave 1/3 + 1, so before Q, the number was (14 + 1) / (2/3) = 22. Similarly working backwards to P and S yields the original number of shells for S.