Practice Questions
In what ratio should sugar costing ₹24/kg and ₹30/kg be mixed to get a mixture worth ₹27/kg?
Alligation rule: $(30-27) : (27-24) = 3:3 = 1:1$.
A container has 40 litres of milk. 10 litres are replaced by water. This process is repeated once more. Find the quantity of milk left.
Final quantity = $40 \times (1 - 10/40)^2 = 40 \times (3/4)^2 = 40 \times 9/16 = 22.5$ litres.
Two solutions contain acid and water in ratio 2:3 and 3:5 respectively. In what ratio must they be mixed to get a solution of ratio 5:8?
Using alligation on acid content: $2/5$ and $3/8$ to get $5/13$. $(5/13 - 3/8) : (2/5 - 5/13) = (40-39)/104 : (26-25)/65 = 1/104 : 1/65 = 65:104 = 5:8$.
A shopkeeper mixes two varieties of rice costing ₹40/kg and ₹60/kg in ratio 3:2. Find the selling price per kg to gain 20%.
Mean Cost Price = $(3 \times 40 + 2 \times 60) / 5 = ₹48$. Selling Price for 20% gain = $48 \times 1.2 = ₹57.6$.
A 60-litre mixture contains 20% alcohol. How much pure alcohol should be added to make it 25%?
Water is 80% of 60 = 48 litres. In the 25% alcohol mixture, water is 75%. New total volume = $48 / 0.75 = 64$ litres. Added alcohol = $64 - 60 = 4$ litres.
In what ratio should tea worth ₹50/kg and ₹70/kg be mixed so that by selling at ₹72/kg a profit of 20% is made?
Selling Price = ₹72, Profit = 20% $\Rightarrow$ Cost Price = $72/1.2 = ₹60$. Ratio = $(70-60) : (60-50) = 10:10 = 1:1$.
Two alloys contain copper and zinc in ratios 3:1 and 1:1. In what ratio should they be mixed to get an alloy with copper and zinc in ratio 5:3?
Copper in A = $3/4 = 75\%$, B = $1/2 = 50\%$, Target = $5/8 = 62.5\%$. Alligation: $(62.5-50) : (75-62.5) = 12.5:12.5 = 1:1$.
A 50L mixture contains milk and water in ratio 3:2. How much water must be added to make the ratio 3:4?
Milk = $30L$, Water = $20L$. Let added water = x. $30/(20+x) = 3/4 \Rightarrow 120 = 60 + 3x \Rightarrow x = 20$L.
A trader mixes two varieties of tea costing ₹80/kg and ₹100/kg in ratio 5:3 and sells at ₹108/kg. Find profit percentage.
CP = $(5×80 + 3×100)/8 = 700/8 = 87.5$. Profit = $(108-87.5)/87.5 × 100 = 20.5/87.5 × 100 ≈ 23.43\%$. Closest option is 25%.
In a 50L mixture of milk and water, the ratio is 3:2. How much water must be added to make the ratio 3:4?
Milk = $30L$, Water = $20L$. Let added water = x. $30/(20+x) = 3/4 \Rightarrow 120 = 60 + 3x \Rightarrow 3x = 60 \Rightarrow x = 20$L.
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