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Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

A fruit salad is made from pineapples, pears, and peaches mixed in the ratio of $2$ to $3$ to $5$, respectively, by weight. What fraction of the mixture by weight is pineapple?

  1. $\dfrac{1}{5}$
  2. $\dfrac{3}{10}$
  3. $\dfrac{2}{5}$
  4. $\dfrac{1}{2}$
  5. $\dfrac{2}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given,
A fruit salad is made from pineapples,pears and peaches mixed in the ratio $2:3:5$ respectively by weight
total weight of mixture as per ratio is $\left( 2+3+5 \right) =10$
Fraction of weight in  mixture  pineapple will be $\dfrac { 2 }{ 10 } =\dfrac { 1 }{ 5 } $
Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

In a family, the father took $\displaystyle\frac{1}{4}$ of the cake and he had $3$ times as much as each of the other members had. The total number of family members is ___________.

  1. $3$
  2. $7$
  3. $10$
  4. $12$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let the number of family members $=x$

fraction of cake the father took $=\dfrac{1}{4}$

fraction of cake  other members had $ =\dfrac{3}{4}$

fraction of cake  EACH  other members had $ =\dfrac{3}{4(x-1)}$

given that :
fraction of cake the father took was 3 times   as much as each of the other members had.
$\Rightarrow  \dfrac{1}{4}=3 \times \dfrac{3}{4(x-1)}$

$\Rightarrow x-1 = 9$
$\Rightarrow x = 10 $

the number of family members are  $=10$


Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

If the fourth proportional of $7\cfrac { 1 }{ 5 } ,4\cfrac { 1 }{ 5 } $ abd $3\cfrac { 6 }{ 7 } $ is k, Then $\cfrac { 4k+1 }{ 4k-1 } =$

  1. $\cfrac { 4 }{ 5 } $
  2. $\cfrac { 6 }{ 5 } $
  3. $\cfrac { 7 }{ 5 } $
  4. $\cfrac { 5 }{ 4 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Convert mixed fractions: 36/5, 21/5, and 27/7. The fourth proportional k satisfies (36/5) / (21/5) = (27/7) / k, which yields k = 9/4. Substituting k into (4k+1)/(4k-1) gives (9+1)/(9-1) = 10/8 = 5/4.