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1.729 ml of combination has coffee and water in the ratio 7:2 how much more water is
to be included to get a new combination has coffee and water in the ratio 7:3?
Facts and ratios
a: b = a/b
Answer : 81 ml
Ratio of coffee and water in 729 ml is 7:2
->Coffee in 729 ml of combination = [(7/9)*(729)] ml = 567 ml
water in 729 ml of combination = 729 – 567 = 162
->If “a” be the some of water included to new combination, with the ratio 7:3
some of water in the new combination= (162 + a )
Then (7/3) = [ (567) / (162+a) ]
=> 7 (162 + a) = 3 x 567
=> 1134 + 7a = 1701
7a = 1701 – 1134
A = 567/7 = 81 ml
Some of water included to new combination = 81 ml.
2. Addition of Rs.312 was divided by100 guys and gals in such a way that the guy
gets Rs.3.60 and each gal Rs.2.40 the number of gals is
Solving simultaneous equations
Answer : 40
-> If “a” be the count of guys and “b” be the count of gals.
Total count of guys and gals = 100
a + b = 100 —Eqn(i)
-> A guy gets Rs.3.60 and a gal gets Rs. 2.40
The money given to 100 guys and gals = Rs. 312
3.60a +2.40b = 312 —Eqn(ii)
->Solving (i) and (ii)
a 3.60 => 3.60 a + 3.60b = 360 (-)
=> 3.60 a + 2.40b = 312
1.20b = 48
B = 48 / 1.20 = 40
Therefore, Count of gals = 40
3. Addition of Rs.36.90 is created by 180 coins which are possibly 10 paise coins or
25paise coins. The count of 10paise coins are
Conversion of Paise into Rupees
Answer : 54 coins
-> Total count of coins = 180
If “a” is count of 10paise coins and “b” be count of 25paise coins
A + b = 180 —Eqn (i)
-> Given 10paise coins and 25paise coins create the addition = Rs. 36.90
[ (10a/100) + (25b/100) ]= 36.90
=> 10a +25b = 3690 ———(ii)
-> Solving (i) and (ii)
a10 => 10 a + 10b = 1800 (-)
=> 10a +25b = 3690
- 15b = -1890
B = 1890 / 15 = 126
Substitute b value in eqn (i) , A = 180 – 126 = 54
Therefore Count of 10paise coins = 54
4. A fraudulent dairy guy declares to market his dairy at price range but he combined it
with water and therefore benefits 25%. The percentage of water in the combination is
Capability Price = { [ (100/(100+benefits%)]a S.P }
The rule of allegation
Needed ratio is less expensive amount: High expensive amount = (d-m): (m-c)
Answer : 20%
-> If Capability Price of 1 L of milk = Rs.1
And S.Price of 1 L of combination = Rs.1
Benefits = 20%
Capability Price of 1 L of combination =[ (100 / 100+25)*1 ]
= Rs. 100/125 = Rs. 4/5
-> From the rule of allegation
i. Capability Price of 1 L of water = 0
ii. Capability Price of 1 L of milk = 1
iii. (p) = 4/5
iv. d – m = 1 – 4/5 = 1/5
v. m – c = 4/5 - 0 = 4/5
Ratio of milk to water = 4/5 : 1/5 = 4:1
% of water in the combination = (1/5 x 100)% = 20%
5. A combination of 20 kg of milk and water contains 10% water. Then how much water
must be included to this combination to increase the % of water to 25%?
Facts of percentage
Answer : 4 kg
-> Some of water in 20 kg of combination is (10/100)*20= 2 kg
-> If “a” kg of water be included with the combination to raise 25% of water
[ (2+a) / (20+a) ] = (25 / 100 )
=> (2 + a ) 100 = 25 (20 + a)
=> 200 + 100a = 500 + 25a
=> 100a – 25a = 500 – 200
=> 75a = 300
A = 4 kg
4 Kg of water is included to this combination.
6. A drum has 40 kg of water, from this drum 4kg of water was taken out and
replaced by milk. This task was repeated nearly 2 times. How much water is now
contained by the drum?
If a drum contains “a” kg of water from which “b” kg is taken out and replaced by milk. After “n” operations, the amount of water = { x[ 1 - (b/a) ]n }kg
Answer : 29.16 kg
Some of water in the Drum a is 40 kg
Some of water taken out b is 4 kg
No.of times = 3
Some of water in the Drum is { a[ 1 - (b/a) ]n }kg
={ 40[ 1 - (4/40) ]3 }kg
= 40 (9/10)3 kg
= 40 ( 729/1000)
Some of water in the Drum = 29.16 kg
7. A drum has a combination of 2 liquids X and Y in the proprtion 7:5 when 9 L of
combination are taken out and the Drum is filled with Y, the proportion of X and Y
becomes 7:9. Then how many litres of liquids X was obtained by the Drum initially?
Facts of combinations and ratios
Answer : 21 L
=> If the Drum has 7a and 5a litres of combinations X and Y correspondingly. Amount of Combination taken out is 9 litres
Some of X in Combination left = [ 7a - (7/12)*9] litres
= [ 7a - (21/4) ] litres
Some of Y in combination left = [ 5a - (5/12)*9 ] litres
= [ 5a - (15/4) ] litres
=> Since the combination is in the ratio 7:9,
{ [7a - (21/4)] / [ 5a - (15/4) ]+9 } = (7/9) => [ (28a - 21) / (20a + 21) ] = (7/9)
=>252a – 189 = 140a + 147
=> 112a = 336
=> a = 3
Some of liquid X, has in the Drum initially is (7*3) = 21 litres
8. The proportion between the current ages of A and B is 6:7. If B is 4 years elder than A, what will be the proportion of the ages of A and B after 4 years?
a. 3 : 5 b. 3 : 4 c. 4 : 3 d. None of these
Facts of ratios
Answer : D) None of the above
If A’s age and B’s age = 6a and 7a years respectively
Then B is 4 years elder than A
=> 7a - 6a = 4
A = 4
After 4 years, A’s age = 6a + 4 years
And B’s age = 7a + 4
Needed ratio = 6a + 4 : 7a + 4
Replace the “a” value of 4
= 28 : 32
= 7 : 8
9. Right now, the proportion between the ages of Karthikh and Kumar is 4 : 3. After 6 years, Karthikh’s age will be 26 years. As of now what is the age of Kumar?
a. 15 years
b. 11 years
c. 16 years
d. 40 years
Answer : A) 15 Years
-> If the current age of Karthikh = 4a
and Kumar =3a correspondingly.
After 6 years , Karthikh’s age = 4a +6 years
-> After 6 years, Karthikh’s age will be 26 years.
4a + 6 = 26
A = (26 - 6) /4 = 5
Kumar’s current age is 3 x 5 = 15 years.
10. The length and breadth of a rectangle are raised in the proportion 3:4 and 4:5 correspondingly. What is the proportion of the previous place to the new?
Area of the rectangle = length * breadth
Answer: 3:5
-> If the real length = 3a
And the real breadth = 4a
Area = (3a)*(4a)
=12 a2
-> New Length is 4a and New breadth is 5a
New area is (4a)*(5a)
= 20 a2
Ratio of previous place to new place = 12 a2 : 20 a2
= 12 : 20
= 3 : 5
