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Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

$Rs. 2430$ are distributed among three persons so that their shares be diminished by $Rs. 5, Rs. 10$ and $Rs. 15$ respectively, the remainder shall be in the ratio $3 : 4 : 5.$ The share of $C$ is

  1. $Rs. 1015$
  2. $Rs. 605$
  3. $Rs. 810$
  4. $Rs. 1415$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let $Rs. 2430$ be divided among three persons with their shares as $x, y$ and $z$ respectively so that $x + y + z = 2430$
Given, $x - 5 : y - 10 : z - 15 = 3 : 4 : 5$
$\Rightarrow x- 5 = 3k, y - 10 = 4k $ and $ z - 15 = 5 k$
$\Rightarrow x = 3k + 5, y = 4k + 10$ and $z = 5k + 15$
$\therefore 3k + 5 + 4k + 10 + 5k + 15 = 2430$
$\Rightarrow 12k + 30 = 2430    \Rightarrow 12 k = 2400 \Rightarrow k = 200$
$\therefore$ C's share $= z = 5k + 15 = 5 \times 200 + 15 = Rs. 1015$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A tiny piggy bank contains Rs. 1, 50 paise, 25 paise  coins in the ratio 1 : 2 : 3. If the total value is Rs. 154, then what is the number of 25 paise coins ?

  1. 168

  2. 112

  3. 56

  4. 156
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratio of coins  = 1 : 2 : 3
Value of the total coin = Rs 154
Let number of one rupee coin is x, 50 paise coin is 2x and 25 paise coin is 3x.
Value of the one rupee coin = x
value of 50 paise coin  =  Rs. $\dfrac{2x}{2}$ = Rs.x
value of the 25 paise coin  = 3x/4
value of whole coins  = 154
x + x + $\dfrac{3x}{4}$ = 154
$8x + 3x = 154 *4$
$11x = 154 *4$
x = 14 *4 = 56. Then
Number of 25 paise coins  = 3x = 3 *56 = 168

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A amount of $Rs.735$ was divided between A,B and C. If each of them had received $Rs.25$ less, their shares would have been in the ratio $1:3:2$. The money received by C was

  1. Rs. $195$
  2. Rs. $200$
  3. Rs. $225$
  4. Rs. $245$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As per the given data,

$(A+25)+(B+25)+(C+25)=735$
$\implies A+B+C=735-75=660$ ....... $(1)$
$A:B:C=1:3:2$
$\implies A=x, B=3x, C=2x$
$\implies x+3x+2x=660$  ...... (From (1))
$\implies x=110$
Money received by C $=2 \times 110 +25=Rs.245$
Hence, option D is correct.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A pot contains $81$ litres of pure milk. $\displaystyle \frac{1}{3} $ of the milk is replaced by the same amount of water. Again $\dfrac{1}{3} $ of the mixture is replaced by that amount of water. The ratio of milk and water in the new mixture is:

  1. $1:2$
  2. $1:1$
  3. $2:1$
  4. $4:5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initially, Milk = 81 litres and waterr = 0 litre Afte 1st operation,
Milk = $ \displaystyle[81 - \frac{1}{3} \times 81] litres = (81 - 27) litres = 54$ litres
Water =  $\displaystyle [ 0+ \frac{1}{3} \times 54] litres $ = $(54-18)$ litres $= 36$ litres
Water= $\displaystyle [27 - \frac{1}{3} \times 27] litres + [\frac{1}{3} \times 54 + \frac{1}{3} \times 27 ] litres$ = $(27-9)$ litres + $(18+9)$ litres $= 45 $litres 
$\therefore $ Required ratio of milk and water in the new mixture $= 36: 45 = 4:5 $

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Divide Rs. $6500$ in two parts, such that if one part is lent out at $9\%$ per annum and other at $10\%$ per annum, the total yearly income(income from simple interest) is Rs.$605$.

  1. $2000,\,4000$
  2. $2000,\,4500$
  3. $1500,\,4000$
  4. $1500,\,4500$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the on one part $=x$

      the other part $6500-x$
$\Longrightarrow \dfrac{9x}{100}+\dfrac{6500-x}{100}\times 10=605$
$\Longrightarrow 9x+65000-10x=60500$
$\Longrightarrow x=4500$
$6500-x=6500-4500=2000$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Rs.$120$ are divided among A,B,C such that A" share is Rs.$20$ more than B"s and Rs.$20$ less than C"s. What is B"s share?

  1. Rs.$10$
  2. Rs.$20$
  3. Rs.$30$
  4. Rs.$40$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C=x. Then $A=\begin{pmatrix}x-20\end{pmatrix}$ and $B=\begin{pmatrix}x-40\end{pmatrix}$.
$x+x-20+x-40=120$ Or $x=60$
$A:B:C=40:20:60=2:1:3$
B"s share $=Rs.120\times \dfrac{1}{6}=Rs.20$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

A, B and C enter into a partnership investing Rs.$35000$, Rs.$45000$ and Rs.$55000$. Find their respective shares in annual profit of $40,500$.

  1. $Rs.10,500,\,Rs.13,500,\,Rs.16,500$
  2. $Rs.11,500,\,Rs.13,500,\,Rs.16,500$
  3. $Rs.10500,\,Rs.12500,\,Rs.16,500$
  4. $Rs.10,500,\,Rs.13,500,\,Rs.14,500$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$A:B:C=35000:45000:55000=7:9:11$
A"s share $=\dfrac{7}{27}\times40500=Rs.10,500$


B"s share $=\dfrac{9}{27}\times40500=Rs.13,500$

C"s share $=\dfrac{11}{27}\times40500=Rs.16,500$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

In a college, the ratio of the number of boys to girls is $8:5$. If there are $200$ girls, the total number of students in the college is

  1. $420$
  2. $520$
  3. $620$
  4. $720$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the boys are $8x$ and Girls are $5x$
$\Rightarrow\;5x=200$
$\Rightarrow\;x=40$
Total students $=8x+5x=13x=13\begin{pmatrix}40\end{pmatrix}=520$