# Simplified ratio and proportion

Posted: Posted Date – 11:59 PM, Thu – Aug 18, 22

Hyderabad: This article follows the last article on the subject of ratios and proportions. Here are some practice questions along with solutions on the subject of ratios and proportions that will help you in your preparation for state government recruiting jobs.
1. Find the 3rd proportional to 9 and 72.

a. 8

b. 216

vs. 576

D. 648

The solution:

In a:b:c, the 3rd proportional is c.
a:b:c can be written a:b::b:c
a:b::b:c can be written a/b = b/c => ; b2 = ca

BC
Here, a:b:c = 9:72:c
∴ 72 x 72 = 9 xc

∴c = 72 x 72/9 = 576

2. Rajesh and Somesh were classmates. Their earnings are now in the 5:6 ratio. Their expense ratio is 7:9. Somesh saves Rs 3,000 every month while Rajesh saves Rs 1,000 more than Somesh. Find the total income and expenses for each of them.
a. Rajesh – 25,000, 21,000; Somesh – 30000, 27000
b. Rajesh – 30,000, 27,000; Somesh – 36000, 32000
vs. Rajesh – 36,000, 32,000; Somesh – 30000, 27000
D. none of these answers
The solution:
Income Ratio = Rajesh: Somesh = 5:6 = 5/6

The common factor helps to easily find the real values

so take ‘A’ as the common factor.

Rajesh’s income = 5A; Somesh’s Income = 6A

Rajesh Expenses = Rajesh Income – Rajesh Saving = 7/9
Somesh Expenses Somesh Income -Somesh Saving

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

∴ 5A-4000/ = 7/

6A-3000 9
∴ 9(5A-4000) = 7(6A-3000)
∴A=5000
Rajesh’s income = 5A = 25000; Somesh’s income = 6A = 30000
Rajesh’s expenses = 25,000 – 4,000 = 21,000
Somesh’s expenses
= 30000 – 3000 = 27000
3. Ram saves Rs 3395 on his salary. He has to pay this money like milk bill, electricity bill and mobile phone bill in ratio 42:32:23. Find the money to pay for each bill.

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

b. Rs.1470, Rs.1120 and Rs.805
vs. Rs.1550, Rs.1235 and Rs.610

D. Rs.1764, Rs.1

The solution:

The common factor helps to easily find the real values
So take ‘A’ as the common factor.
∴ 3 numbers will now be 42A, 32A and 23A
∴ 42A 32A 23A = 3395

∴ 97A = 3395

∴A=35

3 parts of 3395 are

42A=42×35=1470;

32A = 32×35 = 1120
23A = 23×35 = 805
4. Ram and Shyam were carrying money so 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. What is the smaller amount of money of the two?
a. 45
b. 64
vs. 105
D. 120
The solution:
Ratio of original silver numbers = 3:8

The common factor helps to easily find the real values

So take ‘M’ as the common factor.

∴ Original numbers will be 3M and 8M

By adding 5 to them, we get (3M 5) and (8M 5)
∴ 3M 5 = 2/ —————–>; (The ratio of new numbers is 2:5)
8M 5 5
∴ 15M 25 = 16M 10
∴M=15
The smallest monetary 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

vs. p:(qr)

D. (pq):r