Alligation - Study Mode

[#1] In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?
Correct Answer

(D) 4 litres

Explanation

Solution: According to the question, $$eqalign{
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{Milk : Water}} cr
& { ext{Initial Ratio}},,,,,{{ ext{7}}_{ imes 2}}:{3_{ imes 2}} cr
& { ext{Final Ratio}},,,,,,,{{ ext{2}}_{ imes 7}}:{1_{ imes 7}} cr} $$ ∴ Remember water is added not milk, so make milk equal [x08egin{gathered}
,,,,,,,,,,,,,,,,,{ ext{M}},,,,{ ext{:}},,,,{ ext{W}} hfill \
left. x08egin{gathered}
{ ext{Initial}},,,,14,,,,:,,,,6 hfill \
{ ext{Final}},,,,,,14,,,,:,,,,7 hfill \
end{gathered}
ight) hfill \
end{gathered} ]xa0$$eqalign{
& cr
& = ,20,{ ext{unit}} cr
& 1 cr} $$ $$eqalign{
& { ext{20 units = 80 litres}} cr
& { ext{1 unit = 4 litres}} cr
& { ext{Water added = 4 litres}} cr} $$

[#2] 300 kg of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution ?
Correct Answer

(C) 60 kg

Explanation

Solution: In 300 kg of solution, Percentage of sugar = 40% ∴ Sugar = $$frac{{300 imes 40}}{{100}}$$ xa0 = 120 kg Let x kg of sugar be added. Now, according to the question $$eqalign{
& frac{{120 + x}}{{300 + x}} = frac{1}{2} cr
& Rightarrow 240 + 2x = 300 + x cr
& Rightarrow 2x - x = 300 - 240 cr
& Rightarrow x = 60,{ ext{kg}} cr} $$

[#3] The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it. The ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is -
Correct Answer

(B) 40 litres

Explanation

Solution: According to the question, $${ ext{Milk}},,,,:,,,,{ ext{Water}}$$ [left. x08egin{gathered}
,,,,,7,,,,,,,,:,,,,,,,5 hfill \
,,,,,7,,,,,,,,:,,,,,,,8 hfill \
end{gathered}
ight),3,{ ext{unit}}] ∴ Remember water is added and not milk, so make milk equal but here milk is already equal $$eqalign{
& { ext{3 units = 15 litres}} cr
& { ext{1 unit = 5 litres}} cr
& { ext{8 units = 40 litres}} cr} $$ Total quantity of water in the new mixture = 40 litres

[#4] A gold smith has two qualities of gold, one of 12 carats and another of 16 carats purity. In what proportion should he mix both to make an ornament of 15 carats purity ?
Correct Answer

(A) 1 : 3

Explanation

Solution: According to the question, By using alligation method : Ratio of quantity $$ o x08oxed{,,1,,,,,,:,,,,,,3,,}$$

[#5] 7 kg of tea costing Rs. 280 per kg is mixed with 9 kg of tea costing Rs. 240 per kg. The average price per kg of the mixed tea is ?
Correct Answer

(B) Rs. 257.50

Explanation

Solution: According to the question, Average price of mixed tea $$eqalign{
& { ext{ = }}frac{{280 imes 7 + 240 imes 9}}{{16}} cr
& { ext{ = }}frac{{1960 + 2160}}{{16}} cr
& { ext{ = }}frac{{4120}}{{16}} cr
& { ext{ = Rs}}{ ext{. 257}}{ ext{.50}} cr} $$