# QUESTIONS ON RATIO AND PROPORTION (PART-2)

## QUESTIONS ON RATIO AND PROPORTION (PART-2)

#### QUERY 11

**A, B & C are three friends with their incomes in ratio 7 : 9 : 12 and expenditure in 8 : 9 : 15 . If savings of A is 1/4 of his income then find the ratio of their savings?**

A) 56 : 99 : 69

B) 53 : 89 : 69

C) 56 : 89 : 72

D) 64 : 89 : 72

**MAHA GUPTA**

Ratio of incomes is 7 : 9 : 12

Now let their incomes of A, B and C restively are 7,000, 9,000, 12,000

Therefore A’s savings = 1/4 of 7,000 = 1,750

And his expenditure = 7,000 – 1,750 = 5.250

The ratio of their expenditure = 8 : 9 : 15

Now, let expenditure of A, B and C respectively = 8x, 9x and 15x

But A’s expenditure as above = 5,250

Therefore 8x = 5,250

=> x = 5250/8 = 656.25

Thus B’s expenditure is 9*656.25 = 5906.25

And C’s expenditure = 15*656.25 = 9843.75

Now, A’s savings = 1750 (calculated above)

B’s savings = 9000 – 5906.25 = 3093.75

C’s savings = 12000 – 9843.75 = 2156.25

Hence ratio of their savings = 1750 : 3093.75 : 2156:25

56 : 99 : 69 (option ‘A’)

TRICK TO FIND THE RATIO WITH THE HELP OF OPTIONS GIVEN

In the last step, to avoid calculation, we should roughly take the ratio of B and C as 3000 : 2000 = 3 : 2 = 99 : 66

NEAREST to this is only option ‘1’; hence option ‘A’ is correct.

QUERY 12

**A mixture of milk and water is such that the quantity of milk is 3/5 that of water. The proportion of milk in the mixture is?**

A) 3 : 5

B) 5 : 3

C) 2 : 5

D) 3 : 8

**MAHA GUPTA
**Quantity of milk is 3/5 that of water (given)

Now let the quantity of milk in the mixture = 3 units

Therefore the quantity of water in that mixture = 5 units

According to above quantity of mixture = 3+5 = 8 units

Hence the proportion of milk in the mixture = 3/8 = 3 : 8 (option ‘D’)

QUERY 13

**A watermelon is cut into two pieces in the ratio of 3 : 5 by weight. The bigger of the two is further cut in the ratio of 5 : 7 by weight. Find the ratio of each of the three pieces.**

A) 15 : 25 : 26

B) 5 : 7 : 9

C) 2 : 5 : 7

D) 36 : 25 : 35

**MAHA GUPTA**

For easier calculation assume the unit weight of the bigger of first two pieces be the LCM of 3, 5, 5+7=12 i.e. 60.

Now if weight of the bigger of first two pieces = 60 units; the weight of the smaller piece = 36 units [because ratio of the first two pieces is given 3 : 5]

Ratio of the last two pieces which are cut out of the bigger of the first two pieces = 5 : 7

Therefore the weight of the smaller of these = 60*5/12 = 25 units

And the weight of the bigger piece = 60*7/12 = 35 units

Hence ratio of each of the three pieces = 36 : 25 ” 35 (option ‘D’)

QUERY 14

**The prize money of Rs 1800 is divided among three students A, B and C in such a way that 4 times the share of A is equal to 6 times the share of B, which is equal to 3 times the share of C. Find A’s share.**

A) Rs 400

B) Rs 600

C) Rs 700

D) Rs 800

**MAHA GUPTA
** According to the question 4A = 6B = 3C

Now let 4A = 6B = 3C = k

From above, A = k/4; B = k/6; C = k/3

Hence A : B : C = 3 : 2 : 4

Therefore A’s share = 1800*(3/9) = 600 (option ‘B’)

QUERY 15

**Find the third proportional to (x/y + y/x) and √(x² + y²)**

A) xy

B) √(xy)

C) ∛(xy)

D) ∜(xy)

**MAHA GUPTA
** First let one know what the third proportional is

If a : b = b : c, then ‘c’ is called the third proportional to ‘a’ and ‘b’

Obviously in the question given above a = x/y + y/x = (x² + y²)/xy

And b = √(x² + y²)

Therefore the third proportional = b²/a = [√(x² + y²)]²/[(x² + y²)/xy]

= (x² + y²)*xy/(x² + y²) = xy (option ‘A’)

QUERY 16

**Samir’s age is one fourth of his father’s age and two third of his sister Reema’s age. What is the ratio of the age of Samir, Reema and their father respectively.**

A) 10 years

B) 7 years

C) 13 years

D) 8 years

**MAHA GUPTA**

Ratio of Samir’s age to his father = 1 : 4

At the same time Samir’s age is 2/3 of his sister’s age, means 1 : 3/2

Means Samir’s age : Reema’s age : father’s age = 1 : 3/2 : 4

=> 2 : 3 : 8 (option ‘D’)

QUERY 17

**The total salary of A, B and C is Rs 666. If they spend 80%, 85%, 75% of their salaries respectively, their savings are 7 : 6 : 9. Then salary of C is?**

A) Rs 300

B) Rs 250

C) Rs 216

D) Rs 245

**MAHA GUPTA**

Let their salaries respectively be x, y, z

Therefore their savings

A = (100 – 80)% of x = x/5

B = (100 – 85)% of y = 3y/20

C = (100 – 75)% of z = 3z/4

Also their savings ratio = 7 : 6 : 9

=> x/5 : 3y/20 : z/4 = 7 : 6 : 9

=> x = 35; y = 40; z = 36

Hence ratio of the salaries of A, B, C = 35 : 40 : 36

So, C’s salary = 666*(36/111) = 216 (option ‘C’)

QUERY 18

**If (x – a) : (x – b) : (x – c) = 11 : 9 : 5; where x = (a+b+c)/2 then what is a : b : c**

A) 5 : 6 : 9

B) 7 : 8 : 10

C) 8 : 9 : 12

D) 2 : 3 : 5

**MAHA GUPTA**

According to the first equation

(x – a)/11 = (x – b)/9 = (x – c)/5

Now let, (x – a)/11 = (x – b)/9 = (x – c)/5 = k

=> a = x – 11k; b = x – 9k; c = x – 5k

Hence, according to the second given equation = x = [(x – 11k) + (x – 9k) + (x – 5k)]/2

=> x = 25k

Putting this in: a = x – 11k; b = x – 9k; c = x – 5k

a = 14k; b = 16k; c = 20k

=> a : b : c = 14k : 16k : 20k

Therefore, a : b : c = 7 : 8 : 10 (option ‘B’)

NOTE: Such questions are done quickly with the answer options.

QUERY 19

**If a/(b+c) = b/(c+a) = c/(a+b) and a+b+c is not equal to 0; then value of b/(a+b+c) is?**

A) 1/3

B) 5/9

C) 2/7

D) 3/5

**MAHA GUPTA**

Using componendo and dividendo

a/(b+c) = b/(c+a) => (a + b + c)/(a – b – c) = (b + c + a)/(b – c – a)

=> a – b – c = b – c – a

=> a = b

Similarly it can be shown that a = b = c

Taking a = b = c = 1

b/(a+b+c) = 1/(1 + 1 + 1) = 1/3 (option ‘A’)

SHORT

Taking each of a, b, c as 1 satisfies a/(b+c) = b/(c+a) = c/(a+b)

So, b/(a+b+c) = 1/(1 + 1 + 1) = 1/3 (option ‘A’)

QUERY 20

**The ratio of father’s age to his son’s age is 7 : 4. The product of of their ages is 1008. The ratio of their ages 6 years hence will be?**

A) 5 : 3

B) 8 : 5

C) 7 : 4

D) 5 : 8

**MAHA GUPTA**

Let father’s present age is 7x years

Therefore his son’s age = 4x years

Now 7x*4x = 1008

=> 28x² = 1008

=> x = 6

Thus fathers age 6 years hence = 7x + 6 = 7*6 + 6 = 48

And his son’s age 6 years hence = 4x + 6 = 4*6 + 6 = 30

Hence the required ratio = 48 : 30 = 8 : 5 (option ‘B’)