Ratio and proportion made easier

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
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 1,000 more than Somesh. Find the total earnings and expenses of each of them.
a. Rajesh — 25,000, 21,000; Somesh — 30,000, 27,000
b. Rajesh — 30,000, 27,000; Somesh — 36,000, 32,000
c. Rajesh — 36,000, 32,000; Somesh — 30,000, 27,000
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/Expenses of Somesh = Rajesh Income – Rajesh Saving/Somesh Income -Somesh Saving = 7/9
Rajesh save Rs 1,000/- more than Somesh, Rajesh’s savings
= Rs 4,000/-
5A-4000/6A-3000
= 7/9
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. 470, 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. 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

M Venkat
Director
MVK Publications
Dilsukhnagar
7671002120