QUESTIONS ON RATIO AND PROPORTION (PART-1)

QUESTIONS ON RATIO AND PROPORTION (PART-1)

QUERY 1

The ratio of weekly incomes of a and b is 9:7 and the ratio of their expenditures is 4:3.if each saves Rs. 200 per week then the sum of their weekly incomes is ?

A) 3600
B) 3200
C) 4800
D) 5600

Amit jha
Let A ‘s income = 9x

Thus B’s income will be = 7x
Let A’s expense = 4y
Thus B’s expense will be = 3y

Hence the equation for A’s saving: 9x ­­ 4y = 200 …………………………….I

And the equation for B’s saving: 7x ­­ 3y = 200…………………………….II
by solving x = 200

Now the sum of weekly incomes of A and B: 9x+7x=16x
By putting the value of x: = 16 x 200 = 3200 (option ‘B’)

QUERY 2

Rs.600 are divided among A, B and C so that Rs. 40 more than 2/5 of A’s share, Rs. 20 more than 2/7 of B’s share and Rs. 10 more than 9/17 of C’s share are all equal. Find out A’s share?

A) 150
B) 175
C) 400
D) 250

RONNIE BANSAL
According to the question 2/7 of B’s share + Rs 20 = 2/5 of A’s share + Rs 40
So 2/7 of B’s share = 2/5 of A’s share + 20
=> B’s share = 7/2*(2/5) of A’s share + 7/2*20
=> B’s Share = 7/5 of A’s share + 70 …………..i

Again 9/17 of C’s share + 10 = 2/5 of A’s share + 40
=> 9/17 of C’s share = 2/5 share of A’s share + 30
=> C’s share = 17/9*(2/5) 0f A’s share + 17/9*30
=> C’s share = 34/45 of A’s share + 170/3 …………….ii

Now A’s share + B’s share + C’s share + 600
Therefore, A’s share + (7/5 of A’s share + 70) + (34/45 of A’s share + 170/3) = 600
=> (1 + 7/5 + 34/45) of A’s share + (70 + 170/3) = 600
=> 142/45 0f A’s share + 380/3 = 600

Therefore A’s share = 45/142 of (600 — 380/3)= 150 (option ‘A’)

If needed others’ shares also can be calculated easily.

QUERY 3

The marks of 3 students A, B and C are in the ratio 10 : 12 : 15. If the maximum marks of the paper are 100, then the marks of B cannot be in the range of ?

A) 61 to 70
B) 71 to 80
C) 51 to 60
D) 81 to 100

RONNIE BANSAL
C scores the maximum marks because it has the highest ratio, and the maximum marks are 100; so if C scores 100 how much will B score?
Ratio of B and C = 12 : 15 = 4 : 5
Let B gets 4x and C gets 5x

Now assuming C’s score as 100, means 5x = 100
Therefore B’s score = 4x = 80
Hence B cannot get more than 80 marks or we can say his marks cannot be in the range of 81 to 100 (option ‘D’)

NOTE: In an objective exam the range could be written differently, so choose accordingly.

QUERY 4

Brothers A ans B had some savings in the ratio 4:5. They decided to buy a gift for their sister sharing the cost in the ratio 3:4. After they have bought the gift, A spent 2/3 of his amount while B is left with Rs 145. Then the value of the gift is?

A) 140
B) 175
C) 70
D) 105

MRITYUNJAY MAURYA
Let the total savings of both A & B = 9x and the cost of the gift = 7y
Therefore savings of A and B respectively will be 4x and 5x
and their expenditure on the gift respectively will be 3y and 4y

It has been mentioned in the question that ‘A’ spent 2/3 of his amount after the gift had been bought; means he was left with 2/3 of his savings after the gift had been bought and later spent all of it on other things leaving with himself zero. In other words he spent 1 – 2/3 = 1/3 of his savings on the gift.

Now according to the question 1/3 of 4x = 3y
=> x = (9/4)y ……………………………(i)

B is left with Rs 145; which means B’s savings – his expenditure = 145;
or 5x — 4y = 145 ……………………………(ii)

Solving (i) & (ii) for y
y = 20
But the value of he gift is 7y
Hence 7y = 7*20 = 140 (option ‘A’)

QUERY 5

The ratio of earth to water on the entire earth surface is 1:2, and this ratio is 2:3 in the northern hemisphere. The ratio of earth to water in southern hemisphere would be ?

A) 3:11
B) 4:11
C) 11:4
D) 11:3

RONNIE BANSAL
As the ratio of earth to water on the entire surface is 1 : 2; earth and water on the entire surface be 13 and 23 respectively

Now as the northern hemisphere and the southern hemisphere are equal, so total of ‘earth + water’ on each 1/2

Ratio of earth to water on the northern hemisphere is given 2 : 3
Thus, earth on northern hemisphere = 12 × 25 = 15 and water = 12 × 35 = 310

Obviously earth on the southern hemisphere = total of earth – earth on northern hemisphere
=> 1315 = 215

Likewise water on the southern hemisphere = 23310 = 1130
Hence the ratio = 215 : 1130 = 430 : 1130 = 4 :11 (option ‘B’)

QUERY 6

A and B have together three times what B and C have, while A, B, C together have thirty rupees more than that of A. If B has 5 times that of C, then A has?

A) 60
B) 65
C) 75
D) 45

MAHA GUPTA
A, B, C together have thirty rupees more than that of A; means B+C = 30.
But B has 5 times that of C
Therefore B : C= 5 : 1; means B =30*(5/6) = 25 and C = 5

Now A+B = 3(B+C) = 3*30 = 90
But B = 25 (shown above)
Hence A = 90 – 25 = 65 (option ‘B’)

QUERY 7

A bag contains coins of Re 1, Rs 2 and Rs 5 denomination in the ratio of 2 : 3 : 4. If the total amount is Rs 280, find the number of coins of Rs 5 denomination in the bag.

A) 20
B) 30
C) 35
D) 40

MAHA GUPTA
In such sums find always find the value of coins, which can be found multiplying each denomination by its corresponding ratio; and the the ratio of value of coins.

So ratio of value of coins = (1*2) : (2*3) : (5*4) = 2 : 6: 20 = 1: 3 : 10

Now the sum of ratio = 14
But the sum given is 280

So the value of Rs 5 coins = (10/14)*280 = 200
Hence the number of Rs 5 coins = 200/5 = 40 (option ‘D’)

QUERY 8

A bag contains 50p, 1Re and Rs 2 coins in the ratio 2:3:4. If the the total amount is Rs 240 what is the total number of coins?

A) 200
B) 150
C) 180
D) 90

MAHA GUPTA
In such a sum always find the value of each denomination and total number of coins according to the ratio given and add them.

Value of 50p denomination here = (1/2)*2 = Re 1
Value of 1 Re denomination = 1*3 = Rs 3
Value of Rs 2 denomination = 2*4 = Rs 8
So the total value according to the ratio = Rs 12
And the number of coins according to the ratio = 2+3+4 = 9

But the total value in actual = Rs 240

If the value is 12 the number of coins = 9
If the value is 240 the number of coins = (9/12)*240 = 180 (option ‘C’)

QUERY 9

The ratio between the difference of denominator and numerator and the sum of denominator and numerator of a fraction is 2 : 9 . What is the fraction?

A) 7/11
B) 11/7
C) 6/11
D) 2/5

MAHA GUPTA
Let the fraction = x/y

Now according to the question
(y-x)/(y+x) = 2/9
=> 2y+2x = 9y-9x
=> 7y-11x = 0
=> x/y = 7/11 (option ‘A’)

QUERY 10

If (a+b) : (b+c) : (c+a) = 6 : 7 : 8
and a+b+c = 14 then, the value of ‘c’ ?

A) 6
B) 7
C) 8
D) 9

MAHA GUPTA
(a+b) : (b+c) : (c+a) = 6:7:8 (given)

Now let
a+b = 6x ………(i)
b+c= 7x ……….(ii)
c+a = 8x ………(iii)

Now adding all these three equations, (a+b) + (b+c) + (c+a) = 6x + 7x + 8x
=> 2(a+b+c) = 21x
=> 2*14 = 21x                                                                               —(given, a+b+c=14)
=> x= 28/21 = 4/3

From (i)
a+b = 6x = 6*(4/3) = 8

But given, a+b+c = 14
=> (a+b) + c= 14
=> 8 + c = 14

Hence c= 14 – 8 = 6 (option ‘A’)

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