# 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

^{1}⁄

_{3}and

^{2}⁄

_{3}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 = ^{1}⁄_{2} × ^{2}⁄_{5} = ^{1}⁄_{5} and water = ^{1}⁄_{2} × ^{3}⁄_{5} = ^{3}⁄_{10}

Obviously earth on the southern hemisphere = total of earth – earth on northern hemisphere

=> ^{1}⁄_{3} – ^{1}⁄_{5} = ^{2}⁄_{15}

Likewise water on the southern hemisphere = ^{2}⁄_{3} – ^{3}⁄_{10} = ^{11}⁄_{30}

Hence the ratio = ^{2}⁄_{15} : ^{11}⁄_{30} = ^{4}⁄_{30} : ^{11}⁄_{30} = 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’)