MPSC Rajyaseva 2015 CSAT — Question 68

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.