Ratios and Proportions – Quiz 4

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Ratios and Proportions – Quiz 4

Introduction

Ratios and Proportions is one of important topic in Quantitative Aptitude Section. In Ratios and Proportions – Quiz 4 article candidates can find questions with an answer. By solving this questions candidates can improve and maintain, speed, and accuracy in the exams. Ratios and Proportions – Quiz 4 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, Civil Services etc.

Q1

Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
A. 48 B. 24 C. 38 D. None of these

B
Less Cogs ⇒ more turns and less time ⇒ less turns
Name Cogs Time Turns
A 54 45 80
B 32 8 ?

Number of turns required= 80 $\times \frac{54}{32} \times \frac{8}{45}$ = 24 times

Q2

The monthly incomes of A and B are in the ratio 4:5, their expenses are in the ratio 5 : 6. If 'A' saves Rs.25 per month and 'B' saves Rs.50 per month, what are their respective incomes?
A. Rs.400 and Rs.500 B. Rs.240 and Rs.300 C. Rs.240 and Rs.30 D. Rs.440 and Rs.550

A
Let A's income be = 4x
A's expenses, therefore = 4x – 25
Let B's income be = 5x
B's expenses, therefore = 5x – 50
We know that the ratio of their expenses = 5 : 6
$\Rightarrow$ 24x − 150 = 25x − 250
$\Rightarrow$ Therefore, x = 100.
$\Rightarrow$ A's income = 4x = 400 and B's income = 5x = 500

Q3

The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is
A. 2 : 1 B. 5 : 1 C. 99 : 61 D. 227 : 133

D
Proportion of milk in 3 samples is $\frac{2}{3}$, $\frac{3}{5}$, $\frac{5}{8}$
Proportion of water in 3 samples is $\frac{1}{3}$, $\frac{2}{5}$, $\frac{3}{8}$
Since equal quantities are taken,
Total proportion of milk is $\frac{2}{3}$ + $\frac{3}{5}$ + $\frac{5}{8}$ = $\frac{227}{120}$
Total proportion of water is $\frac{1}{3}$ + $\frac{2}{5}$ + $\frac{3}{8}$ = $\frac{133}{120}$
Proportion of milk and water in the solution is = 227 : 133

Q4

A, B and C play cricket. A's runs are to B's runs and B's runs are to C's as 3:2. They get altogether 342 runs. How many runs did A make?
A. 162 B. 108 C. 72 D. None

A
A : B = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4 (making B equal)
Therefore, A : B : C = 9 : 6 : 4
Therefore, the runs made by A= $\frac{9}{19} \times 342$ = 162

Q5

Points A and B are both in the line segment PQ and on the same side of its midpoint. A divides PQ in the ratio 2:3, and B divides PQ in the ratio 3:4. If AB=2, then the length of PQ is:
A. 70 B. 75 C. 80 D. 85

A
Let PA = 2x and AB = 3x
and PB = 3y and BQ = 4y
PB : BQ = 3 : 4
PA : QA = 2 : 3
PQ = 5x = 7y
x = $\frac{7}{5}$.....(i)
From equation (i) and (ii),
Now, AB = PQ − PA − BQ = 7y − 4y − 2x
$\Rightarrow$3y − 2x = 2 -------------- (ii)
y = 10 and Hence, PQ = 70