# Ratio & Proportion

Quantitative Aptitude Questions and Answers section on “Ratio & Proportion” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.
1.

There are four numbers in the ratio of 1:2:3:4. The sum of these four numbers is 16, then sum of first and fourth number is :
[A]5
[B]8
[C]10
[D]80

8
Sum of first and fourth number is :
$\because \left [ \frac{1}{10}+\frac{4}{10} \right ]\times 16=8$
Hence option [B] is the right answer.

2.

If $x=\frac{1}{3}y$ and $y=\frac{1}{2}z$, Then x:y:z is equals to :
[A]3:2:1
[B]1:2:6
[C]1:3:6
[D]2:4:6

1:3:6
$\because x=\frac{1}{3}y, y=\frac{1}{2}z$
$\therefore x:y=1:3$ and $y:z=1:2=3:6$
$\therefore x:y:z=1:3:6$
Hence option [C] is the right answer.

3.

Find the mean propotional to 6 and 24;
[A]16
[B]12
[C]8
[D]20

12
Mean propotional between 6 and 24 = $\sqrt{6\times 24}=\sqrt{144}=12$
Hence option [B] is the right answer.

4.

If 0.75:x::5:8, Then find x
[A]1.6
[B]0.46
[C]1.2
[D]0.48

1.2
Because we know that :-
Product of means = Product of extremes
Thus, a:b::c:d<=>$\left ( b\times c \right )=\left ( a\times d \right )$
So in this question we can write:
$5\times x=8\times 0.75$
$\therefore 5x=6$
$=> x=\frac{6}{5}=1.2$

5.

If a:b=5:9 and b:c=6:11; Then Find a:c
[A]11:34
[B]10:33
[C]12:33
[D]None of these

10:33
$\because a:c=\frac{a}{c}=\frac{a}{b}\times \frac{b}{c}$
$=> \frac{5}{9}\times \frac{6}{11}=\frac{10}{33}$
$=> \frac{a}{c}=\frac{10}{31}$
=> a:c=10:31
Hence option [B] is the right answer.

6.

If a:b=5:9 and b:c=6:11; Then Find a:b:c
[A]5:6:11
[B]5:9:11
[C]10:18:11
[D]10:18:33

10:18:33
$\because a:b=5:9, b:c=6:11=6\times \frac{9}{6}:11\times \frac{9}{6}=9:\frac{33}{2}$
$\therefore a:b:c=5:9:\frac{33}{2}=10:18:33$
Hence option [A] is the right answer.

7.

If a:b=5:7, find (3a+5b):(5a-2b)
[A]50:9
[B]40:9
[C]50:11
[D]40:11

50:11
$\because \frac{a}{b}=\frac{5}{7}$
$\therefore \frac{\left ( 3a+5b \right )}{5a-2b}=\frac{3\left ( \frac{a}{b} \right )+5}{5\left ( \frac{a}{b} \right )-2}$
$=>\frac{3\times \frac{5}{7}+5}{5\times \frac{5}{7}-2}=\frac{50}{11}$
$=>a:b=50:11$
Hence option [C] is the right answer.

8.

If $a:b=\frac{2}{9}:\frac{1}{3}, b:c=\frac{2}{7}:\frac{5}{14}$ and $d:c=\frac{7}{10}:\frac{3}{15}$, then find a:b:c:d
[A]56:84:30:30
[B]16:24:30:35
[C]56:24:30:30
[D]56:24:30:35

16:24:30:35
$\because a:b=2:3, b:c=4:5$ and $c:d=6:7$
=>$a:b=2:3, b:c=1:\frac{5}{4}$ and $c:d=1:\frac{7}{6}$
=>$a:b=2:3, b:c=3:\frac{15}{4}$ and $c:d=\frac{15}{4}:\frac{7}{6}\times \frac{15}{4}$
=>$a:b=2:3, b:c=3:\frac{15}{4}$ and $c:d=\frac{15}{4}:\frac{35}{8}$
=>$a:b:c:d:=2:3:\frac{15}{4}:\frac{35}{8}=16:24:30:35$
Hence option [B] is the tight answer.

9.

Devide 675 Rs. in the ratio 5:4
[A]300, 375
[B]325, 350
[C]340, 335
[D]375, 300

375, 300
Sum of ratio terms : (5+4)=9
$\therefore$ First Part = $\left [ 675\times \frac{5}{9} \right ]$=375 Rs.
And Second part = $\left [ 675\times \frac{4}{9} \right ]$=300 Rs.
Hence option [D] is the right answer.

10.

Devide 952 Rs. among a, b, c in the ratio 37:18:13
[A]502, 252, 198
[B]502, 260, 190
[C]518, 252, 182
[D]518, 234, 200

518, 252, 182
Sum of ratio terms:37+18+13=68.
A’s share=$\left [ 952\times \frac{37}{68} \right ]$=518 Rs.
B’s share=$\left [ 952\times \frac{18}{68} \right ]$=252 Rs.
C’s share=$\left [ 952\times \frac{13}{68} \right ]$=182 Rs.
Hence option [C] is the right answer.