# Ratio and proportion made easier

Published: Published Date - 11:59 PM, Thu - 18 August 22

**Hyderabad:** This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions on the ratio and proportion topic that will help you in your preparation for the State government recruitment jobs.

**1. Find the 3rd proportional to 9 and 72.**

a. 8

b. 216

c. 576

d. 648

Ans: c

Solution:

In a:b:c, 3rd proportional is c.

a:b:c can be written as a:b::b:c

a:b::b:c can be written as a/b = b/c =>; b2 = ac

b c

Here, a:b:c = 9:72:c

∴ 72 x 72 = 9 x c

∴ c = 72 x 72/9 = 576

**2. Rajesh and Somesh were classmates. Their earnings now are in the ratio 5:6. The ratio of their expenses is 7:9. Somesh saves Rs 3,000 every month while Rajesh saves Rs 1000 more than Somesh. Find the total earnings and expenses of each of them.**

a. Rajesh – 25000, 21000; Somesh – 30000, 27000

b. Rajesh – 30000, 27000; Somesh – 36000, 32000

c. Rajesh – 36000, 32000; Somesh – 30000, 27000

d. None of the above

Ans: a

Solution:

Income ratio = Rajesh : Somesh = 5:6 = 5/6

Common factor helps in finding actual values easily

so, take ‘A’ as common factor.

Income of Rajesh = 5A; Income of Somesh = 6A

Expenses of Rajesh = Rajesh Income – Rajesh Saving = 7/9

Expenses of Somesh Somesh Income -Somesh Saving

Since Rajesh save, Rs 1000/- more than Somesh, Rajesh’s savings = Rs 4000/-

∴ 5A-4000/ = 7/

6A-3000 9

∴ 9(5A-4000) = 7(6A-3000)

∴ A = 5000

Income of Rajesh = 5A = 25000 ; Income of Somesh = 6A = 30000

Spending of Rajesh =25000 – 4000 = 21000

Spending of Somesh

= 30000 – 3000 = 27000

**3. Ram saves Rs 3395 from his salary. He needs to pay this money as milk bill, electricity bill and mobile phone bill in the ratio 42 : 32 : 23. Find the money to be paid for each bill.**

a. Rs.1245, Rs.1150 and Rs.1000

b. Rs.1470, Rs.1120 and Rs.805

c. Rs.1550, Rs.1235 and Rs.610

d. Rs.1764, Rs.1

Ans: b

Solution:

Common factor helps in finding actual values easily

So, take ‘A’ as common factor.

∴ 3 numbers will now be 42A, 32A and 23A

∴ 42A 32A 23 A = 3395

∴ 97A = 3395

∴ A = 35

3 parts of 3395 are

42A = 42 x 35 = 1470;

32A = 32 x 35 = 1120

23A = 23 x 35 = 805

**4. Ram and Shyam were carrying some money such that their money was in the ratio 3:8. A friend gives each of them Rs.5 and their money is now in the ratio 2:5. Which is the smaller money of the two?**

a. 45

b. 64

c. 105

d. 120

Ans: a

Solution:

Ratio of original money numbers = 3:8

Common factor helps in finding actual values easily

So, take ‘M’ as common factor.

∴ Original numbers will be 3M and 8M

Adding 5 to them, we get (3M 5) and (8M 5)

∴ 3M 5 = 2/ —————–>; (Ratio of new numbers is 2:5)

8M 5 5

∴ 15M 25 = 16M 10

∴ M = 15

Smaller money value is 3M = 3 x 15 = 45

**5. If u : v = w : x = y : z = 1:2, then, (pu qw ry) : (pv qx rz) is equal to:**

a. 1:2

b. 2:1

c. p:(q r)

d. (p q):r

Ans: a

**To be continued**

**M. Venkat**

**Director**

**MVK Publications**

**Dilsukhnagar**

**7671002120**