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In what ratio should a shopkeeper mix two types of rice, one costing ₹20 per kg and another costing ₹40 per kg to get a rice variety costing ₹ 28 per kg?

Solution

✅ Correct Option: 2

A shopkeeper has two types of rice:

  • Cheaper rice: ₹20 per kg
  • Expensive rice: ₹40 per kg

The goal is to mix them to get rice costing ₹28 per kg.


Using the alligation method:

Cheaper Rice          Mixture          Expensive Rice
    ₹20          →    ₹28    ←            ₹40

Finding the differences:

Difference 1: 28−20=828 - 20 = 8

Difference 2: 40−28=1240 - 28 = 12


The ratio of cheaper rice to expensive rice is obtained by cross-matching the differences:

Cheaper Rice : Expensive Rice =12:8= 12 : 8

Simplifying by dividing both by 4:

Cheaper Rice : Expensive Rice =3:2= 3 : 2


Checking with 3 kg of ₹20 rice and 2 kg of ₹40 rice:

Total cost =3×20+2×40= 3 \times 20 + 2 \times 40

=60+80= 60 + 80

=140= 140

Total weight =3+2=5= 3 + 2 = 5 kg

Average price =1405=28= \dfrac{140}{5} = 28 per kg


The shopkeeper should mix the cheaper rice (₹20 per kg) and expensive rice (₹40 per kg) in the ratio 3:23:2.

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