RATIO AND PROPORTION
Problem1: a:b = 3:4, b:c = 5:2, find a:b:c ?
Problem2: a:b = 1:3, b:c = 2:5, c:d = 2:3 find a:b:c:d ?
Problem3: There are two types of mixtures of milk and water. In the first mixture, out of 12lt. of mixture, 5lt. of milk only and in second mixture, 6lt. is milk and 12lt. is water. Which one is better in terms of milk strength ?
a. 12
b. 15
c. 18
d. None of these
Problem4: A cat takes 7 steps for every 5 steps of a dog, but 5 steps of a dog are equal to 6 steps of a cat. What is the ratio of speed of cat to that of a dog ?
a. 6:7
b. 7:6
c. 6:5
d. None of these
Problem5: Q3. The value of coin varies directly to the square of its radius, when its thickness is constant. The radius of a coin is 1.5cm when its value is rp. 2. What will be the radius of a coin if its value is rp. 5 ?
Problem6: A started business with rp. 26,000. After 3 months B joined him with his rp. 16,000. After some more time C joined them with rp. 25,000. At the end of the year, out of a total profit of rp. 15,543, C gets rp. 3825 as his share. How many months after B joined the business did C join ?
Problem7: A started business with rp. 52,000 and after 4 months, B joined him with rp. 39,000. At the end of the year, out of the total profits B received total rp. 20,000 including 25% of the profit as commission for managing the business. What amount did A receive ?
Problem8: A working partner gets 20% as his commission of the profit after his commission is paid. If the working partner’s commission is 8,000rp . then what is the total profit in the business?
Problem9: A milkman has a mixture of milk in which the ratio of milk and water is 5:3. He sells 40lt. of milk, i.e. mixture then he adds up 15lts of pure water. Now the ratio of milk and water is 5:4. What is the new quantity of mixture?
a. 72lt
b. 270lt
c. 135lt
d. Data insufficient
Problem10: A naughty student breaks the pencil in such a way that the ratio of two broken pieces is same as that of the original length of the pencil to one of the larger part of the pencil. The ratio of the other part to the original length of the pencil is ?
Problem11: 6 pumps of Kirlosker can fill a tank in 7 days and 2 similar pumps of Usha can fill the tank in 18 days. What is the ratio of the efficiency of Kirlosker pump to that of Usha pump ?
a. 6:7
b. 7:6
c. 7:54
d. Cant be determined
Problem12: Petrol is 7 times heavy than kerosene and castor mobil is 18 times as heavy as kerosene. What should be the ratio of petrol and castor mobil in the new mixture to get a new mixture which must be 11 times as heavy as kerosene ?
Problem13: A goldsmith has 361 rings of gold. He sells some of them at a loss of 4% and others at a profit of 15% making overall profit of 8%. Find the number of rings sold at a profit of 15%?
a. 171
b. 133
c. 218
d. 278
Problem14: If (a+b) : (b+c) : (c+a) = 5:6:9, and a+b+c = 10, then find the value of c ?
Problem15: The students in three classes are in the ratio of 2:3:4. If 40 students are added in each class, the ratio becomes 4:5:6. Find the total number of students in all the three classes is ?
a. 270
b. 180
c. 126
d. 135
#Answers
1.Solution: way other then conventional way
3----4
5----2
3*5 : 5*4 : 4*2 --> 15:20:8
3*5 --> first column multiplication
5*4 --> diagonal multiplication
4*2 --> second column multiplication
2.Solution:
A___b___c___d
1___3
___2____5
________2___3
Step2:
A___b___c___d
1___3____3___3
2___2____5___5
2___2____2___3
Step3: multiply columns
1*2*2 : 3*2*2 : 3*5*2 : 3*5*3 --> 4:12:30:45
3.Solution: first mixture--> 5/12
Second mixture -> 6/18
Let total mixture be the lcm of 12 and 18 i.e. 36lt.
Now the quantity of milk in first mixture would be, 5*36/12 -->15lt.
In second mixture, 6*36/18 --> 12lt.
4.Solution:
speed: cat and dog is 7 steps to 5 steps
length of 5 steps of a dog = length of 6 steps of a cat
length covered by dog is to cat is 6/5
in each step a dog will cover 6/5 times a distance than that of a cat
ratio of actual speed of cat is to dog is 7:5*6/5
7:6
5.Sol: V proportional to r^2
V = kr^2 (k be a constant here)
2 = k(1.5)^2
K= 2/2.5 --> 8/9
Now, 5 = 8(r)^2/9
R^2= 5*9/8
R= 3/2 *sqrt(5/2) --> 1.5*sqrt(2.5) --> 1.5*1.6
R= 2.4cm (approx.)
6.Sol: ratio of the share of the profits --> 26000*12 : 16000*9 : 25000*C
312:144:25C
C’s share --> 25C/(456 + 25C) = 3825/15453
On solving, C=6
It means C joined 3 months later than B joined.
7.Sol: profit share of A and B = 52000*12 : 39000*8
2:1
Let profit be x
B receives 25% as commission (0.25x)
Rest 0.75x is being divided among A and B in the ratio 2:1
A --> 0.50x
b--> 0.25x
B’s total share would be 0.25x + 0.25x --> 0.50x
0.50x --> 20,000
X --> 40,000
So A will get 20,000.
8.Sol: total profit be X
After paying commission, remaining profit will be x-8000
20/100 * (8000-x) = 8000
On sloving, we will get value of x as 48,000.
9.Sol: 40lt is taken out from the mixture in the ratio --> 5:3
Means 25lt of milk is taken out and 15lt taken out from water
Milk be 5x
Water be 3x
5x-25/3x-15+15 = 5/4
X=20
Old mixture --> 8*20 --> 160lt
Remaining mixture --> 160 – 40 +15 --> 135lts
10.Sol: let pencil be broken into two parts a and b
a/b = a+b/a
a^2 = ab + b^2
a^2 – b^2 –ab =0
let b now be 1
a:b = a:1
a^2 – a -1 =0
a = 1 + sqrt5/2 (by solving quad, and taking positive value only)
now as in qs askd, a/b = 1+ sqrt5/2 :1
a:b = 1 + sqrt5 : 2
b/ (a+b) = 2/ (1 + sqrt5) = 2/(3+ sqrt5)
11. Sol: efficiency of one K pump: eff of one U pump = 6*7/2*18 = 6:7
12.Sol: the best way to do such type of qs is by allegation
7-------------------18
---------11-----------
(18-11)------------(11-7) ____________ take cross difference
7-------------------4
7:4
13.Sol: again use allegation in this qs
(-)4--------------------------(+) 15
---------------(+)8-----------------
7-------------------------------12
(-4 and +8 we don’t have to subtract, you just have to check the difference between them, like u can check in number line, on number line we will see the difference between the -4 and +8 will be 12…)
The ratio will be 7:12
We have to find the number of rings sold at 15% profit.
12*361/19 --> 228
Ans.
14.Sol: (a+b) : (b+c) : (c+a) = 5x : 6x : 9x
2(a+b+c) = 20x
(a+b+c)=10x
Given in qs (a+b+c)=10
So value of x will be 1
Now, c = (a+b+c) – (a+b)
C = 10-5 --> 5
Ans.
15. Sol: 2:3:4 --> 4:5:6
Whenever there is similar increment in all the quantities like in this qs,
2 --> 4
3 --> 5
4 --> 6
Increment of 2 in all..
Now 2x = 40
X --> 20
Total number of students, 9x --> 9*20 --> 180
Ans.
Problem1: a:b = 3:4, b:c = 5:2, find a:b:c ?
Problem2: a:b = 1:3, b:c = 2:5, c:d = 2:3 find a:b:c:d ?
Problem3: There are two types of mixtures of milk and water. In the first mixture, out of 12lt. of mixture, 5lt. of milk only and in second mixture, 6lt. is milk and 12lt. is water. Which one is better in terms of milk strength ?
a. 12
b. 15
c. 18
d. None of these
Problem4: A cat takes 7 steps for every 5 steps of a dog, but 5 steps of a dog are equal to 6 steps of a cat. What is the ratio of speed of cat to that of a dog ?
a. 6:7
b. 7:6
c. 6:5
d. None of these
Problem5: Q3. The value of coin varies directly to the square of its radius, when its thickness is constant. The radius of a coin is 1.5cm when its value is rp. 2. What will be the radius of a coin if its value is rp. 5 ?
Problem6: A started business with rp. 26,000. After 3 months B joined him with his rp. 16,000. After some more time C joined them with rp. 25,000. At the end of the year, out of a total profit of rp. 15,543, C gets rp. 3825 as his share. How many months after B joined the business did C join ?
Problem7: A started business with rp. 52,000 and after 4 months, B joined him with rp. 39,000. At the end of the year, out of the total profits B received total rp. 20,000 including 25% of the profit as commission for managing the business. What amount did A receive ?
Problem8: A working partner gets 20% as his commission of the profit after his commission is paid. If the working partner’s commission is 8,000rp . then what is the total profit in the business?
Problem9: A milkman has a mixture of milk in which the ratio of milk and water is 5:3. He sells 40lt. of milk, i.e. mixture then he adds up 15lts of pure water. Now the ratio of milk and water is 5:4. What is the new quantity of mixture?
a. 72lt
b. 270lt
c. 135lt
d. Data insufficient
Problem10: A naughty student breaks the pencil in such a way that the ratio of two broken pieces is same as that of the original length of the pencil to one of the larger part of the pencil. The ratio of the other part to the original length of the pencil is ?
Problem11: 6 pumps of Kirlosker can fill a tank in 7 days and 2 similar pumps of Usha can fill the tank in 18 days. What is the ratio of the efficiency of Kirlosker pump to that of Usha pump ?
a. 6:7
b. 7:6
c. 7:54
d. Cant be determined
Problem12: Petrol is 7 times heavy than kerosene and castor mobil is 18 times as heavy as kerosene. What should be the ratio of petrol and castor mobil in the new mixture to get a new mixture which must be 11 times as heavy as kerosene ?
Problem13: A goldsmith has 361 rings of gold. He sells some of them at a loss of 4% and others at a profit of 15% making overall profit of 8%. Find the number of rings sold at a profit of 15%?
a. 171
b. 133
c. 218
d. 278
Problem14: If (a+b) : (b+c) : (c+a) = 5:6:9, and a+b+c = 10, then find the value of c ?
Problem15: The students in three classes are in the ratio of 2:3:4. If 40 students are added in each class, the ratio becomes 4:5:6. Find the total number of students in all the three classes is ?
a. 270
b. 180
c. 126
d. 135
#Answers
1.Solution: way other then conventional way
3----4
5----2
3*5 : 5*4 : 4*2 --> 15:20:8
3*5 --> first column multiplication
5*4 --> diagonal multiplication
4*2 --> second column multiplication
2.Solution:
A___b___c___d
1___3
___2____5
________2___3
Step2:
A___b___c___d
1___3____3___3
2___2____5___5
2___2____2___3
Step3: multiply columns
1*2*2 : 3*2*2 : 3*5*2 : 3*5*3 --> 4:12:30:45
3.Solution: first mixture--> 5/12
Second mixture -> 6/18
Let total mixture be the lcm of 12 and 18 i.e. 36lt.
Now the quantity of milk in first mixture would be, 5*36/12 -->15lt.
In second mixture, 6*36/18 --> 12lt.
4.Solution:
speed: cat and dog is 7 steps to 5 steps
length of 5 steps of a dog = length of 6 steps of a cat
length covered by dog is to cat is 6/5
in each step a dog will cover 6/5 times a distance than that of a cat
ratio of actual speed of cat is to dog is 7:5*6/5
7:6
5.Sol: V proportional to r^2
V = kr^2 (k be a constant here)
2 = k(1.5)^2
K= 2/2.5 --> 8/9
Now, 5 = 8(r)^2/9
R^2= 5*9/8
R= 3/2 *sqrt(5/2) --> 1.5*sqrt(2.5) --> 1.5*1.6
R= 2.4cm (approx.)
6.Sol: ratio of the share of the profits --> 26000*12 : 16000*9 : 25000*C
312:144:25C
C’s share --> 25C/(456 + 25C) = 3825/15453
On solving, C=6
It means C joined 3 months later than B joined.
7.Sol: profit share of A and B = 52000*12 : 39000*8
2:1
Let profit be x
B receives 25% as commission (0.25x)
Rest 0.75x is being divided among A and B in the ratio 2:1
A --> 0.50x
b--> 0.25x
B’s total share would be 0.25x + 0.25x --> 0.50x
0.50x --> 20,000
X --> 40,000
So A will get 20,000.
8.Sol: total profit be X
After paying commission, remaining profit will be x-8000
20/100 * (8000-x) = 8000
On sloving, we will get value of x as 48,000.
9.Sol: 40lt is taken out from the mixture in the ratio --> 5:3
Means 25lt of milk is taken out and 15lt taken out from water
Milk be 5x
Water be 3x
5x-25/3x-15+15 = 5/4
X=20
Old mixture --> 8*20 --> 160lt
Remaining mixture --> 160 – 40 +15 --> 135lts
10.Sol: let pencil be broken into two parts a and b
a/b = a+b/a
a^2 = ab + b^2
a^2 – b^2 –ab =0
let b now be 1
a:b = a:1
a^2 – a -1 =0
a = 1 + sqrt5/2 (by solving quad, and taking positive value only)
now as in qs askd, a/b = 1+ sqrt5/2 :1
a:b = 1 + sqrt5 : 2
b/ (a+b) = 2/ (1 + sqrt5) = 2/(3+ sqrt5)
11. Sol: efficiency of one K pump: eff of one U pump = 6*7/2*18 = 6:7
12.Sol: the best way to do such type of qs is by allegation
7-------------------18
---------11-----------
(18-11)------------(11-7) ____________ take cross difference
7-------------------4
7:4
13.Sol: again use allegation in this qs
(-)4--------------------------(+) 15
---------------(+)8-----------------
7-------------------------------12
(-4 and +8 we don’t have to subtract, you just have to check the difference between them, like u can check in number line, on number line we will see the difference between the -4 and +8 will be 12…)
The ratio will be 7:12
We have to find the number of rings sold at 15% profit.
12*361/19 --> 228
Ans.
14.Sol: (a+b) : (b+c) : (c+a) = 5x : 6x : 9x
2(a+b+c) = 20x
(a+b+c)=10x
Given in qs (a+b+c)=10
So value of x will be 1
Now, c = (a+b+c) – (a+b)
C = 10-5 --> 5
Ans.
15. Sol: 2:3:4 --> 4:5:6
Whenever there is similar increment in all the quantities like in this qs,
2 --> 4
3 --> 5
4 --> 6
Increment of 2 in all..
Now 2x = 40
X --> 20
Total number of students, 9x --> 9*20 --> 180
Ans.
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