RATIO AND PROPORTION
34. The income of ABC are in the ratio 3:7:4 and there expenditures are in the ratio 4:3:5.if A saves
300 out of an income of rs 2400. The savings of B and c are
Rs 4025 and rs 575
Rs 1575 and rs 2625
Rs 2750 and rs 1525
Rs 3725 and rs 1525
A B C
Incomes 3 7 4
Expenditures 4 3 5
Savings 300
A is saving 300 out of 2400 means out o f income and this means 2400 is As income
3 parts is equal to 2400 and one part is 800
This gives 3 parts of As income 2400
This gives 7 parts of Bs income 5600
This gives 4 parts of Cs income 3200
A s expenditure is 2400 – 300 = 2100
4 parts is equalto 2100
One part is 2100/4 = 525
As expenditure is 4 * 525 =2100
Bs expenditure is 3*525 = 1575
Cs expenditure is 5 * 525 = 2625
Bs saving = 5600-1575 = 4025
C s saving = 3200- 2625= 575
RATIO AND PROPORTION
35. A and B have money in the ratio 2:1 .if A gives RS 2 to B ,the money will be in the ratio 1:1 what
were the initial amounts they had.
Rs 12 and Rs 6
Rs 16 and RS 8
Rs 8 and RS 4
Rs 6 and RS 3
Check options 12-2 :6+2 =10:8 not correct
16-2:8 +2= 14:10 not correct
8-2:4+2 = 6:6 correct
36. By mistake instead of deviding the Rs 117 among ABC in to the ratio ½ : 1/3 : 1/4 .it was
devided in to 2:3:4 who gains most and how much?]
A,Rs 28
B,Rs 3
C,Rs 20
C, Rs 25
½: 1:3 : 1/4 = 3*4:2*4:3*2 = 12:8:6 = 6:4:3
Deviding 117 in 6 : 4 :3 =
13 parts equal to 117
1 part is 117/13
Then 6 parts of A =6*117/13 = 6 * 9=54
Then 4 parts of B = 4*117/13 = 36
Then 3 parts of C = 3 * 9 = 27
But it was devide in to 2:3:4
A got 2 * 117/9 = 26
B got 3* 117/9 = 39
C got 4* 117/9 = 52
C got 24 extra…25
RATIO AND PROPORTION
37.Between two consecutive years my incomes are in the ratio of 2:3 and expenses are in the
ratio of 5:9 if my income in the second year is 45000 and my expenses in the first year is rs
25000 my total savings for the two years is ?
Nil
15000
10000
5000
1styear 2nd year
Incomes 2 3
Expenditures 5 9
Income in the second year is 45000 means for 3 parts 45000 for 1 part 15000. 1 st year income
is of 2 parts means 2*15000 = 30000.
Expenditure in the first year is 25000 ..means for 5 parts 25000 and for 1 part means 5000.
Expenditure in the 2nd year is of 9 parts so 9*5000 = 45000
1st year savings first year income – firt year expenditure = 30000-25000=5000
2nd year savings second year income –second year expenditure= 45000-45000 =0
Total savings = 5000
38.RS 180 contained in a box consist of 1 rupee ,50 paise and 25 paise coins in the ratio 2:3:4
.what is the number of 50 paise coins ?
60
120
150
180
1 rupee 50 paise 25 paise
2 3 4
RATIO AND PROPORTION
Just devide by how many coins need them for single rupee notation
For 1 rupee 2 5o paise coins
For 1 rupee 4 25 paise coins
So
Ratio becomes
2/1: 3/2:4:4
4:3:2
For total 9 parts give 180 rupees
1 par 20
80 : 60: 40
Meas 60 rupees of 5o paisa coins ..means In number 60*2 = 120
Just in question he is given the ratio in nos we converting to 1 rupee and finding the requied
value. And again converting into no of coins …
39. The numerator and denominator of the fraction are in the ratio 2:3 if 6 is substracted from
the numerator the results is a fraction that has a value 2/3 of the original function.the
numerator of the original function
6
18
27
36
Original fraction is 2x/3x and when 6 is substracted from the numerator
2x-6/3x= 2/3(2x/3x)
2x-6 /3x =4/9
18x-54=12x
6x=54
X=9
The numerator is 18 denominator is 27
RATIO AND PROPORTION
40.
p = r = t = 2
q s u 3
thebn mp+nr+ot is equal to =
mq+ns+ou
p=2/3q r=2/3s t=2/3u
2/3( mq+ns+ou)
(mq+ns+oq)
=2/3
Fourth propotional of 0.12,0.21,8
0.12 : 0.21 = 8 : x
0,12 * x = 8* 0.21
=14
RATIO AND PROPORTION
41.
A and B have monthly income s in the ratio 5:6 and monthly
Expenditures are in the ratio 3:4 if they save rs 1800 and rs 1600 respectively find the monthly
income B
3400
2700
1720
7200
Incomes are in the ratio 5:6 means incomes 5x and 6x
Income – expenditures = savings
5x-1800 = 3
6x-1600 4
20x- 7200 = 18x-4800 => 2x= 2400 => x=1200
So monthly income of B is 6*1200 7200
42.
Zinc and copper are in the ratio of 5:3 in 200 gram of alloy how much grams of copper be added to
make
The ratio to as 3:5 ?
400 1 72 66
3 200
Method 1
Zinc and copper in the ratio 5:3 means total 5+3=8 parts is equalto 200 1 part is 25
Zinc which is 5 parts means 25*5 = 125
Copper which means 25*3 =75
Zinc/copper = 125 = 35 gives x=400/3
75+x
RATIO AND PROPORTION
METHOD 2
Not changed value is zinc equate the zinc quantity
First it was 5 parts in total o f 8 parts of 200 grams = 3 parts in total of 8 parts of X grams
5/8 * 200 = 3/8 *x => x= 1000/3 but first 200 and now 1000/3
The difference gives the added quantity of copper. 1000/3 -200 = 1000-600
That is 400/3
43.
The student s in three classes are in the ratio 2:3:5 .if 40 students are increased in each class the ratio
changes to 4:5:7 originally the total number of students was
100
180
200
400
2x+40 =4
3x+40 5
10x+200 =12x+160
X=20
Means ratio 2:3:5 total parts are 2+3+5 = 10 1 part is 20 10 parts are 200 total no of students are 200
44.
In 30 liters mixture of acid the ratio of acid and water is 2:3 what amount of water should be added
to the mixture so that the ratio of acid and water becomes 2:5 ?
10 15 19 12
RATIO AND PROPORTION
Acid is not changing equate the quanities in both
2/5 *30= 2/7 *x => x=42 but the change of 42-30 is water so 12 is answer
The product of two positive integers is 1575 and there ratio is 9:7 the smaller one is ?
25,35,45,70
Numbers are 7x and 9x so the prouduct will be come 63x2 = 1575 => x=5 smallest 7x = 35
45.
In alloy the ratio of copper and zinc is 5:2 if 1.250kg of zinc is mixed in 17 kg 500g of alloy then the
ratio of copper and zinc will be
2:1
2:3
3:2
1:2
Equating copper content
In 17.5 kg alloy copper is 5/7 * 17.5 that is equa to 5/7*35/2
1.250 is mixed to 17.5 that it will becom 18.75 = 17 +1/2 + 1+1/4 = 18 ¾ = 75/4
Take copper to total ratio as a/b then
5/7 *35/2 = a/b * 75/4
a/b = 2/3 copper is 2 total is 3 means copper to zinc ratio is 2:1
46.
the ratio of number of boys to that of girls in a group becomes 2:1 when 15 girls leave .But after wards
when 45 boys also leave ,the ratio becomes 1:5 originally the number girls in the group was
20
30
40
50
RATIO AND PROPORTION
Boys are x and girls are y …15 girls left making girls y-15 then the ratio becomes 2:1
x/y-15 = 2:1 2y-30=x
45 boys left making boys x-45 then the ratio becomes 1:5
x-45 = 1
y-15 5
5x-225 = y-15 => 10y -150-225 =y-15
9y =360 y=40
47.Same quantity of rice is required for each member of a family of 15 members .on a particular day
due to the obscence of sum members of the family the consumption of rice was reduce d in the ratio
the number of memberson that day obsent was
In question it is given is in the ratio 5:3 means for 5 people 3 persons reduced but here 15 people
means 9 people reduced.
48. The ratio of first and second class train fares between two stations is 3:1 and that of the number of
passengers travelling between the two stations by first and second classes is 1:50 if on a particular day
Rs 1325 are collected from passengers travelling between the two stations then the amount collected
from the second class passenger is
1,250
1000
850
750
Here we need to take
Ratio of collections of 1st to 2nd = ratio of fares * ratio of no of passengers
RATIO AND PROPORTION
=3*1: 1*50
= 3:50
Total collection 53 parts is equalto 1325
1 part is 1325/53
50 parts 1325/53 * 50
=25*50
= 1250
49. When a particular number is substracted from each of 7,9,11 and 15 the resulting numbers are in
proportion the number to be substracted is
7 : 9 : : 11:15
By checking options 6*14 =8*10 not
5*10= 7*9 not
4*12=6*8 yes
