1. 15 litres of a mixture of milk and water in the ratio 2:1, the amount of milk added to the mixture so as to have milk and water in the ratio 5:2 ?
Solution:-
2. 72 litres of a mixture contains milk and water in the ratio of 27:5. How much more water is to be added to get a mixture containing milk and water in the ratio 3:1 ?
Solution:-
3. A mixture contains milk and water in the ratio 5:1, on adding 5L of water the ratio of milk and water becomes 5:2. Find the quantity of milk in the mixture?
Solution:-
milk = 5x
water = x
\(\frac{{5x}}{{x + 5}} = \frac{5}{2}\)
10x = 5x + 25
x = 5
∴ milk = 5×5 = 25L Ans
4. Nickel and copper are in the ratio 5:3 in 264 gm of an alloy. How much gram of copper be added to make the ratio 3:5 ?
Solution:-
5. An alloy contains copper, zinc and nickel in the ratio of 5:3:2. The quantity of Nickel that must be added to 200 kg of this alloy to have the new ratio 5:3:3.
Solution:-
6. Two numbers are in the ratio 2:3. If 3 is subtracted from the first and 3 is added to the second the ratio becomes 1:2. Then find the sum of the numbers.
Solution:-
Let 1ˢᵗ number = 2x
& 2ⁿᵈ number = 3x
\(\frac{{2x – 3}}{{3x + 3}} = \frac{1}{2}\)
⇒ 4x – 6 = 3x + 3
⇒ x = 9
∴ 1ˢᵗ number = 2×9 = 18
& 2ⁿᵈ number = 3×9 = 27
∴ Sum of two numbers = 18 + 27
= 45 Ans
7. A trader has 50 kg of rice, a part of which he sells at 28% profit and rest at 12% loss. On the whole his loss is 8%. What is the quantity sold at 28% profit and that at 12% loss ?
Solution:-
8. Four vessels of equal size contains mixture of milk & water. The concentration of milk in four vessel is 60%, 70%, 75%, 80% respectively. If all the four mixtures are mixed then find th ratio of milk to water in the resultant mixture ?
Solution:-
Ans
9. A 49 litres cylinder contains a mixture of oxygen and nitrogen, the volume of oxygen being 49% of total volume. A few litre of the mixture is released and an equal amount of nitrogen is added. Then the same amount of mixture as before is released and replaced by nitrogen for the second time. As a result the oxygen content becomes 25% of the total volume. How many litres of mixture is released each time?
Solution:-
⟹ x = 147 Ans
10. There are two vessels of equal capacity one full of milk and second one-third full of water. The second vessel is then filled up by the first, the contents of the second are then poured back into the first till it is full and then again the contents of the first ar poured in the second till it is full. What is the proportion of milk in the second vessel ?
Solution:-
Assume vol. of each vessel 18L.
1ˢᵗ case: When \(\frac{2}{3}^{rd}\) of 1ˢᵗ vessel i.e.\(\frac{2}{3} \times 18 = 12L\) milk is poured in 2ⁿᵈ vessel
2ⁿᵈ case: When \(\frac{2}{3}^{rd}\) of the second vessel is poured in 1ˢᵗ vessel.
3ʳᵈ case: When \(\frac{2}{3}^{rd}\) of the first vessel is poured in 2ⁿᵈ vessel.
∴ In 2ⁿᵈ vessel m : w = 20 : 7
∴ Proportion of milk in final mixture = 20 : 20 + 7 = 20 : 27 Ans