Question 1 1 / -0
If A : B = 3 : 4, B : C = 5 : 6 and C : D = 11 : 9, find the value of A : D.
Solution
=
,
=
&
=
⇒
=
⇒
=
=
⇒ A : D = 55 : 72
Question 2 1 / -0
If a : b = 3 : 4, then (6a + b) : (4a + 5b) is equal to
Solution
Now,
=
... (2)
Put the value of a/b in equation (2) from (1).
∴
=
=
=
Question 3 1 / -0
If 2x = 3y = 4z, then x : y : z is equal to
Solution
Let 2x = 3y = 4z = k
∴ x =
, y =
& z =
x : y : z =
:
:
= 6k : 4k : 3k = 6 : 4 : 3
Question 4 1 / -0
The ratio of number of boys and girls in a school of 720 students is 7 : 5. How many more girls should be admitted to make the ratio 1 : 1?
Solution
B : G = 7 : 5
Total number of boys and girls = 720
7x + 5x = 720
⇒ x =
= 60
Number of boys = 420
Number of girls = 300
Let the number of girls to be added be y.
So,
y = 420 - 300 = 120
Question 5 1 / -0
In a mixture of 60 litres, the ratio of milk to water is 2 : 1. If the ratio of milk to water needs to be 1 : 2, then the amount of water (in litres) to be added further is
Solution
Amount of mixture = 60 litres
Ratio of milk to water = 2 : 1
⇒
=
Let the amount of added water be x litres to make the ratio of milk to water 1 : 2.
=
⇒ x = 60 litres
Amount of water to be added = 60 litres
Question 6 1 / -0
The ratio of A's money to B's money is 3 : 7 and the ratio of B's money to C's money is 2 : 1. If A has $600, C has
Solution
A : B = 3 : 7 and B : C = 2 : 1
Therefore, A : B : C = 3 × 2 : 7 × 2 : 7 × 1 = 6 : 14 : 7
Let amount with A = 6x, with B = 14x and with C = 7x
Now, 6x = 600
x = 100
Therefore, amount with C = 7x = $700
Question 7 1 / -0
The sum of two numbers is 40 and their difference is 4. Find the ratio of the numbers.
Solution
Let x and y be numbers.
\ x + y = 40 …..(1)
x – y = 4 .........(2)
Add (1) and (2), we get
2x = 44
x = 22
Put the value of x in (1), we get y = 18
Therefore, the required ratio =
Question 8 1 / -0
A profit of $84 is divided between A and B in the ratio of
:
. What amount will A and B get?
Solution
x +
x = 84
x = 84 ⇒ 7x = 84 × 12 ⇒ x =
= 144
∴ A will get =
× 144 = $48
B will get =
× 144 = $36
Question 9 1 / -0
If a : b = 2 : 3, b : c = 3 : 4, c : d = 4 : 5, find a : b : c : d.
Solution
=
... (i)
... (ii)
... (iii)
Here, the value of b is same in (i) and (ii). In the same way, the value of c is same in (ii) and (iii).
Taking values of b and c common, we get
a : b : c : d = 2 : 3 : 4 : 5
Question 10 1 / -0
If A walks 5 km in 2 hours and B walks 500 m in 45 minutes, find the ratio of their speeds.
Solution
Speed of A in km/hr = 5 km/2hrs
Speed of B in km/hr =
/
=
×
=
km/hr
\ Ratio of speeds of A and B =
:
= 15 : 4
Question 11 1 / -0
The sum of three numbers is 98. The ratio of the first two numbers is 2 : 3 and that of the last two numbers is 5 : 8. Find the 2nd number.
Solution
Let the numbers be x, y and z.
x + y + z = 98
Also, x : y = 2 : 3 and y : z = 5 : 8
Therefore, x : y : z = 10 : 15 : 24
Let x = 10k, y = 15k and z = 24k
Then, 10k + 15k + 24k = 98
k = 2
The numbers are 20, 30 and 48.
Hence, second number is 30.
Question 12 1 / -0
The marks scored by Steve and Tony bears a ratio 3 : 5 and the difference between their marks is 32. Find their individual marks.
Solution
Let the marks scored by Steve and Tony is 3x and 5x respectively.
Also 5x - 3x = 32 {According to question}
\ 2x = 32
x = 16
Hence individual marks are 48, 80
Question 13 1 / -0
David gave a portion of his money to Arnold. Arnold in turn gave one-third of what he received to Rosy and Rosy gave one half of what she received to Pat. If Pat got $5, how much money did David have?
Solution
Since David gave a portion of his money to Arnold & no information has been provided regarding this portion.
Question 14 1 / -0
Find two numbers which are in the ratio 3 : 4 and when 7 is subtracted from each, the remainders are in the ratio 2 : 3.
Solution
Let the first number be 3x and the second number be 4x.
According to the question:
⇒ 3(3x - 7) = 2(4x - 7)
⇒ 9x - 21 = 8x - 14
⇒ x = 7
Hence,
First number = 3x = 21
Second number = 4x = 28
Question 15 1 / -0
A, B and C brought mangoes in the ratio 5 : 3 : 2. If the difference between number of mangoes with A and C is 60, then find the difference between the number of mangoes with B and C.
Solution
Let the respective number of mangoes brought by A, B and C be 5x, 3x and 2x.
Question 16 1 / -0
A bag contains 25-cent, 10-cent and 5-cent coins in the ratio 1 : 2 : 3, respectively. If the total value of the coins is $36, the number of 25-cent coins is (1 $ = 100 cents)
Solution
Let x be the number of 25-cent coins.
Question 17 1 / -0
Instead of dividing $117 among
A ,
B and
C in the ratio
, we divided the sum in the ratio 2 : 3 : 4. Who gained the most and by what amount?
Solution
First, if we divide $117 in the ratio
among
A ,
B and
C .
Then
A :
B :
C = 6 : 4 : 3
Let
A 's share = 6
x ,
B 's share = 4
x and
C 's share = 3
x Therefore, 6
x + 4
x + 3
x = 117
x = 9
Share of
A = $54, share of
B = $36, share of
C = $27
Now, let us divide $117 in the ratio 2 : 3 : 4.
Let the share of
A = 2
y , share of
B = 3
y and share of
C = 4
y Therefore, 2
y + 3
y + 4
y = 117
y = 13
Share of
A = $26, Share of
B = $39 and Share of
C = $52
Therefore,
C gained the most, i.e., 52 - 27 = $25
Question 18 1 / -0
Two numbers are in the ratio 5 : 7. If nine is subtracted from each of them, their ratio becomes 7 : 11. Find the numbers.
Solution
Given: Ratio of two numbers = 5:7
Let the first number be 5x and the second be 7x.
Now, according to the question,
11(5x - 9) = 7(7x - 9)
55x - 99 = 49x - 63
6x = 36
Or, x = 6
Therefore, the first number = 5x = 30 and the second number = 7x = 42
Question 19 1 / -0
If 1,000 copies of a book of 13 sheets require 26 reams of paper, how many reams of paper are required for 5,000 copies of a book of 17 sheets?
Solution
1000 copies of 13 sheets require 26 reams of paper.
Let 5000 copies of 17 sheets require x reams of papers.
×
=
x =
= 170
Question 20 1 / -0
In an agricultural farm, there are 3618 trees consisting of cashew nut, mango and coconut trees in the ratio 1 : 3 : 5. Find the number of mango trees in the farm.
Solution
Let the number of trees of cashew nut, mango and coconut be x, 3x and 5x, respectively.
x + 3x + 5x = 3618
⇒ 9x = 3618
⇒ x =
= 402
Number of mango trees in the farm = 3 x 402 = 1206
Question 21 1 / -0
A sum of Rs. 407 is to be divided among A, B and C so that their shares are in the ratio
. Find their respective shares.
Solution
Ratio of shares of A, B and C =
= 15 : 12 : 10
Let A's share = 15x, B's share = 12x and C's share = 10x
Therefore, 15x + 12x + 10x = 407
x = 11
Hence, share of A = 15x = Rs. 165
Share of B = 12x = Rs. 132
Share of C = 10x = Rs. 110
Question 22 1 / -0
In what proportion must wheat at $1.80 per kg be mixed with wheat at $2.50 per kg, so that the mixture be worth $2.0 per kg?
Solution
Applying the rule of alligation,
⇒ Required proportion = 5 : 2
Question 23 1 / -0
An alloy contains 24% of tin by weight. How much more tin to the nearest kg must be added to 100 kg of the alloy so that the percentage of tin will be doubled?
Solution
Let X kg of tin be added to the alloy
Tin (kg) Alloy (kg) 24 100 24 + X 100 + X
⇒ (24 + X) / (100 + X) = 2 (24 / 100)
⇒ X = 46 (nearest)
Question 24 1 / -0
A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio of milk and water becomes 5 : 2. Find the quantity of milk in the original mixture.
Solution
Let the quantity of milk be 5X and of water be X.
Question 25 1 / -0
Metals X and Y are to be used for making two different alloys. If the ratio of weights of X and Y in the first alloy is 6 : 5 and that in the second alloy is 7 : 13, then how many kg of X metal must be melted along with 11 kg of the first alloy and 20 kg of the second alloy to produce a new alloy containing 40% of metal Y?
Solution
Let x kg of metal X be added.
Weight of metal X in the 1
st alloy = 6 kg
Weight of metal X in the 2
nd alloy = 7 kg
Total weight of the new alloy = (11 + 20 + x) kg
Total weight of metal X in the new alloy = (6 + 7 + x) kg
According to the question,
On solving, we get
x = 14 kg
×
Sign in
Profile
Signout
Get latest Exam Updates 
