Get a grip on arithmetic problems

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.

The salary of Charan and Raju is in the ratio of 5 : 4. If the salary of each is increased by Rs 3,000, then their new ratio becomes 6 : 5. What is the salary of Charan?
a) Rs 12,500 b) Rs 12,000
c) Rs 15,500 d) Rs 15,000
Ans: d
Solution: 5 : 4
|     |
6 : 5
1 part —> 3000
5 parts —> ?
5 × 3000 = Rs 15,000

Which of the following should be added to each of the four numbers 4, 8, 12, 22 to make them proportional?
a) 3/4 b) 4/3
c) 3/8 d) 8/3

Ans: b

Solution: Let the number = k
4+k / 8+k = 12+k /22+k
88+4k+22k+k² = 96+12k+8k+k²+
88+26k = 96+20k
6k = 8
k = 8/6
k = 4/3

If a, b, c and d are in continued proportion, then (ma³+nb³ -rc³) : (mb³+nc³ – rd³) =
a) a : d b) d : a
c) b : c d) c : b

Ans: a

Solution: a/b = b/c = c/d = k
c = dk, b = ck, a = bk
b = (dk)k
b = dk²
Since, a = bk
—> a = (dk)²k
a/d = k³
(i) = (ma³+nb³ -rc³) / (mb³+nc³ – rd³) =
= {m(dk³)³+n(dk²)³ -r(dk)³) : (m(dk²)³+ n(dk)³ – rd³) =
= k³
From (i)
k³ = a/d
= a : d

If a : b = c : d, then ma+nc / mb+nd is equal to
a) a : b b) b : a
c) m : n d) n : m

Ans: a

Solution: Let a/b =
c/d = k
a = bk, c = dk
= ma+nc /mb+nd = mbk+ndk / mb+nd
= k(mb+nd) / mb+nd
= k
k = a/b
= a : b
To get the ratio p : q (for p  q) one has to add a number to each term of the ratio x : y. The number is
a) px+qy / p – q
b) qx – py / p – q
c) px – qy / p – q
d) py – qx / p – q

Ans: b

Solution: Let the number to be
added be a
x+a / y+a = p/q
qx+aq = py+­ap
qx – py = a (p – q)
a = qx – py /
p – q