1. Find the fourth proportional to the
numbers 8,12 and 16
Explanation: The fourth proportion of a,b and c is bc/a
Therefore, fourth proportional of 8,12 and
16 = 12x16 /8 = 24
2. What is the third proportional to
18, 12?
Explnation: Third proportion of a and b is b2/a
Third proportion of 18 and 12
= 122/18 = 8
3. What is the mean proportional
between 16 and 25 ?
Explnation: The mean proportional of a and b is sqrt (ab)
Therefore, mean
proportion of 16 and 25 is = sqrt(16 x 25) = sqrt(400)= 20
4. If A:B = 3:1 and B:C = 2:3 . What is
the value of A:B:C?
Explnation: In
the given 2 ratios, the common term is B. To write the two ratios into a single
ratio, the values of the common term must be equal.
A : B : C A : B : C
3 :
1 x
2 6 : 2
2: 3
2 : 3
6 : 2 : 3
5. If A:B=2:5 , B:C = 5:4
and C:D = 6:1. Then what is the value of A : D ?
Explanation: A/B x
B/C x C/D = A/D Therefore A:D = 2/ 5 x 5/4 x
6/1 = 3/1 = 3:1
6. Rs 3798 is divided into parts in the
ratio of 5:4. What is the value of the 1st
part?
Explanation:: Divided in the ratio= 5:4 Sum of the parts= 5+4= 9
1st
part = Rs 3798 = 5/9 = Rs 2110
7. A sum of money is divided between A
and B in the ratio of 11:3 . The difference between their shares is Rs 6400.
Find the total amount?
Explanation: : Let
A and B got 11x and 3x .
The difference between their shares
11x – 3x = 8x =6400 =>x = 800
Total amount= Sum of the shares = 11x + 3x
=> 14x = 14 x 800 =Rs 11200
8. The sum of the two numbers is 72.
Which of the following cannot be the ratio of those two numbers ?
a)8:1 b ) 5:3 c)11:7 d)7:3
Explanation: The sum of the numbers is
72.
The sum of the terms of the ratio must
divide the sum of the numbers.
Taking option 1 : Sum of the terms =
8+1 = 9 which divides 72.
Taking option 2 : Sum of the terams =
5 +3 = 8 which divides 72.
Taking option 3: Sum of the terms = 11
+7 = 18 which divides 72
Taking option 4: Sum of the terms =
7+3 = 10 which is not factor of 72.
So this cannot the required ratio.
9. The price of a TV and a Radio are in
the ratio of 7:2. If a T.V. costs 25000 more than a Radio, find the price of
the T.V.?
Explanation : When TV costs more than the radio by Rs 25000
means , the difference between the price of T.V. and Radio is Rs 25000
Prices of TV and
Radio are in the ratio 7:2. Let their prices be 7x and 2x.
The difference of
their prices => 7x-2x => 5x = Rs 25000=> x= Rs 5000
The price of the
TV => 7x = 7 x 5000 = Rs 35000
10.
Rs 2400
is divided among A, B and C . Half of the A’s share , 1/3 of the B’s share and
1/5 th of the C’s share are equal. Then find the share of C?
Explanation: ½ A = 1/3 B = 1/5 C are equal. We say they
are equal to k
½ A = 1/3 B = 1/5 C= k Therefore A=2k B= 3k and C=5k.
The ratio of the
shares of A,B and C = 2k :3k: 5K= 2:3:5
The share of C = Rs 2400 x 5/10 = Rs 1200
11.
Rs 3720
is divided into three parts in proportional to the fractions ½ : 1/3 : 1/5 .
What is the second part?
Explanation: 1/2: 1/3: 1/5 = 15/30 : 10/30:6/30
The required ratio = 15: 10:6 Therefore, second part = Rs 3720 x
10/31 =Rs 1200
12.
Two
numbers are in the ratio of 4:5 and their product is 500.Find the bigger number?
Explanation: Let
two numbers be 4x and 5x.
Product of the numbers =>4x x 5x => 20x2
= 500
=> x2
= 25 =>x=5
Bigger number = 5x= 5 x 5 = 25
13.
Three
numbers are in the ratio 5:4:3 such that the sum of their squares is 0. What is
the smallest number?
Explanation: The
numbers are in the ratio of 5:4:3.
Let numbers be
5x,4x and 3x. Given that sum of their squares is 450
Sum of their
squares = (5x)2+(4x)2+(3x)2
ð 25x2 + 16 x2 + 9 x2
= 450
ð 50 x2 =450
ð x2=9
ð x=3
Smallest number = 3x = 3 x 3 =9
14.
Rs 3120
is divided among A,B and C so that 3 times the A’s share, and twice the B’s
share and 4 times of the C’s share are equal. Find the share of A ?
Solution: 3 times
the A’s share, and twice the B’s share and 4 times of the C’s share are equal
3A = 2B= 4C = k
A =k/3 ,
B=k/2 C= k/4 => A:B:C = k/3: k/2:k/4
A: B : C = 4:6:3 /12
The required
ratio = 4:6:3
Share of A = Rs 3120 x 4/13 = Rs 960
15.
Rs 7820
are divided among A, B and C so that A receives 5/12 as much as B and C
together receive and B receives 4/13 as much as A and C together receive. Find
the difference between the shares of A and B ?
Solution : A
receives 5/12 as much as B and C together receive.
A = 5/12(B+C)=> A : (B+C)= 5:12
A’s share = Rs 7820 x 5/17 =Rs 2300
B receives 4/13
as much as A and C together receive
B = 4/13(A+C)=> B: (A+C)= 4:13
B’s share = Rs 7820 x 4/17= Rs 1840
Difference between A and B’s share = Rs
2300 –Rs 1840 =Rs 460
16.
Rs 12200 divided among
5 women, 4 boys and 7 men , such that the share a woman, a boy and a man are in the ratio of 7:3:2. Find the share
of a girl?
Explanation : Let the share of a woman , a boy and that of
man are 7x ,3x and 2x.
Total amount paid = (5 x 7x) + (4 x 3x) +(7
x 2x) =61x = 12200
=>35x+12x+14x=12200
=>61x=12200
=>x=200
The share of a girl= 3x = 3 x Rs 200 = Rs
600
17.
A bag
consists of 1 rupee, 50 paise and 25p coins and their total value in rupees is
Rs 1120 .These three types of coins are in the ratio 3:20:4. How may 25 paisa
coins are there?
Explanation : The coins are 1 rupee, 50 paisa and 25 paisa.
The ratio is 100p: 50
p : 25 p =4 : 2: 1
The coins are in the
ratio = 3 :20: 4
The ratio of
their values in rupees=>
12 :40 :4
The value of 25 p coins in total Rs 1120
= 1120 x 4/56= 80 rupees
Number of 25 p coins are = 80x4 = 320 coins
18.
A bag
contains one rupee, 50 paisa and 10 paisa coins in the ratio of 3:2:1. How many
50 paisa coins are there, if the total
number of money in the bag is Rs 820?
Explanation : Let the number of 100p, 50p and 10p coins be 3x ,2x and x .
The ratio of the values of coins = 100 p: 50p
:10 p = 10:5:1
Total amount = (10 x 3x ) +
(5 x 2x) +( 1 x x) =
30x+10x+x=41x
The ratio of their values in rupees=
30x:10x:x
Given total amount is Rs 820 => 41x = 820
=> x=Rs 20
Total value of 50p coins (in rupees) =
10 x 20 =Rs 200
Total 50 paisa coins are = 200 x 2 = 400
coins
19.
Two
numbers are in the ratio 2:5. If each number is increased by 12, the ratio
becomes 4:7.Find the two numbers?
Explanation : Let
the numbers be 2x and 5x.
2x+ 12 / 5x+12 = 4/7
ð 7(2x+12) = 4(5x+12)
ð 14x+84 = 20x+48
ð 6x=36
x=6
The numbers are 2x and 5x = 2 x 6 and 5 x 6
=12 and 30
20.
Two
numbers are in the ratio 3:2. If 20 is subtracted from each of them, the ratio
becomes 5:3. Find the numbers
Explanation : Let two numbers be 3x and 2x.
3x-20 / 2x-20 =
5:3
ð 3
(3x-20) = 5 (2x-20)
ð 9x -60 = 10x- 100 X= 40
Therefore, the
numbers are 3x and 2x -= 3x40 and 2x40=120 and 80
21.
Two
vessels of equal capacity are 8/11 and 3/5 full of wine. They are then filled
up with water and the contents are poured in another vessel. Find the ratio of
the wine and water in the final mixture?
Explanation: 8/11 th of first vessel and 3/5 th of second
vessel have wine.
Quantity of wine
in 1st vessel = 8/11
Quantity of water in 1st vessel = 3/11
Quantity of wine
in 2nd vessel =3/5
Quantity of water in 2nd vessel = 2/5
Total quantity of wine = 8/11 + 3/5 =73/55 Total quantity of water = 3/11 +2/5 =
37/55
Ratio of wine and
water in final mixture= 73 : 37
22.
In a
mixture of 90 litres wine and water are in the ratio 3:2. If 12 litres of water
is added to the mixture, what will be the ratio of wine and water in the final
mixture?
Explanation :
Quantity of wine in mixture = 90 x 3/5 = 54 litres
Quantity of water in the mixture = 90 x 2/5 =
36 lifters
When 12 liters of
water is added to the mixture, quantity of water = 36 +12 = 48 litres
Ratio of wine and
water in the final mixture= 54 : 48 =9:8
23.
The
marks of a and b are in the ratio of 3:2 and marks of b and c are in the ratio
of 7:1 and sum of the marks of a,b and c is 1480. Find the marks of A?
Explanation: A : B = 3 :2
B: C
= 7 :1
Equating the
common term B, the ratio of A,B and C =
21 :14:2
Total marks obtained by A,B and C= 1480
Marks of A = 1480 x 21/37 = 840
24.
What is
the number which when subtracted from the terms of the ratio 5:9 makes it equal
to 1:3 ?
Explanation: Let the number to be subtracted = x
5-x / 9-x = 1/3 =>3(5-x) =1(9-x)=> 15-3x = 9-x=> x=3
The number to be
subtracted from the terms of the ratio 5:9 to make it ratio 1:3 is 3
25.
The
incomes of A and B are in the ratio of 3:2 and their expenditures are in the
ratio of 5:3. If each of A and B saves Rs 2000 , the find the income of A?
Explanation : Income – Savings = Expenditures
Let the incomes of A and B be 3x and 2x
respectively.
Each of A and B saves Rs 2000.
3x-2000 / 2x -2000 = 5:3
ð 3(3x-2000)= 5(2x-2000)
ð 9x-6000= 10x-10000
ð X=4000
Income of A =3x = 3 x 4000 = Rs 12000
26.
An
organization reduces the number of employees in the ratio of 9:7 and increases
their salaries in the ratio of 10:13. Find in what ratio the expenditure of
that organization on salaries is changed and also find the difference between
the present and previous expenditures on salaries, if it was previously Rs 5400
lacs.
Explanation: Ratio
of the employees = 9:7
Ratio of the salaries = 10 :13.
Ratio of previous
and present expenditures on salaries
= 9 x 10: 7 x 13
= 90 :91
Therefore, salaries will increase in the
ratio of 90:91.
Expenditure on salaries
previously => 90x = 5400 lacs
Expenditure on
salaries now => 91x = 5400/90 x 91 =5460
Therefore, the difference is = Rs 5460 –Rs
5400 = 60 lacs
27.
Ratio
of the fares of first, second and third class tickets of a train is 3:2:1 and
ratio of number of passengers travel in first , second and third classes is
2:3:4 . If the total collection from 2nd class tickets is Rs 12000,
find the total collection from 3rd class tickets?
Explanation: Ratio of the fare of 1st, 2nd
and 3rd class tickets = 3 : 2 :1
Ratio of the passengers travel in
these classes = 2 : 3 :4
The ratio of total collection from 1st,
2nd and 3rd class= 3x2 + 2x3 + 1x4
=6:6:4=
3:3:2
Collection from 2nd class
tickets = 3x=12000 =>x=4000
Total collection from 3rd
class tickets = 2x = 2 x 4000 = Rs 8000
28.
48 litres
of mixture contains milk and water in the ratio 5:1. How much water must be
added to this mixture so as to have milk in the ratio 2:1?
Explanation : The quantity of milk in 48 litres of mixture
= 48 x 5/6=40 litres
Quantity of water in the mixture = 48-
40 = 8 litres
We have to add water . So there is no change
in the quantity of milk.
Milk/ Water = 40/8+x = 2/1
ð 1 x 40 =2( 8+x)
ð 40= 16+x => x= 12
29.
A vessel of 270 litres
capacity is full of pure wine. On the first day 1/3 of the milk is drawn and
filled with water on the second day 1/3 of the mixture is drawn and filled with
water and again the same thing done on the third day. Find the quantity of wine
and water at the end?
Solution: Total
pure wine = 270 litres
When 1/3 is
drawn, we will have 2/3 of the previous wine.
Quantity of wine at the end = 270 x 2/3 x
2/3 x 2/3
= 80 litres
Quantity of water = 270-80= 190 litres
30.
A sum
of Rs 45 is made up of 100 coins partly of 50 paisa and partly of 25 paise.How
many 25 paisa coins are there?
Solution : Let
the number of 50 paisa coins and 25 paisa coins be x and y respectively.
Number of coins => x+ y = 100 ------- (1)
Value of coins => 50x +25y = 4500 ----(2)
Solving equations 1 and 2 , we get x=80 and y=20
So the number of
25 paisa coins are 20.
