edited by
629 views
1 votes
1 votes

The income of Amala is $20\%$ more than that of Bimala and $20\%$ less than that of Kamala. If Kamala's income goes down by $4\%$ and Bimala’s goes up by $10\%$, then the percentage by which Kamala's income would exceed Bimala’s is nearest to

  1. $31$
  2. $28$
  3. $32$
  4. $29$
edited by

1 Answer

1 votes
1 votes

Let the income of Bimala $ = 100x $

The income of Amala is $20\%$ more than that of Bimala.

So, the income of Amala $ = 100x \times \frac{120}{100} = 120x $

The ratio of Bimala and Amala $ = 100x : 120x = 5:6 \quad \longrightarrow (1)$

Let the income of Kamala $ = 100y $

The income of Amala $20\%$ less than that of Kamala.

So, the income of Amala $ = 100y \times \frac{80}{100} = 80x $

The ratio fo Kamala and Amala $ = 100y : 80y = 5:4 \quad \longrightarrow (2) $

Now, combining equation $(1)$ and $(2)$, we get

  • Bimala : Amala $ = (5 : 6) \times 4 = 20: 24$ 
  • Kamala : Amala $ = (5 : 4) \times 6 = 30: 24$

The ratio of Bimala : Amala : Kamala $ = 20 : 24 : 30 = 10 : 12 : 15 $

If Kamala's income goes down by $4\%$ and Bimala’s goes up by $10\%$. Then,

  • Kamala’s income $ = 15 \times \frac{96}{100} = 14 . 4 $
  • Bimala’s income $ = 10 \times \frac {110}{100} = 11 $

$\therefore$ The percentage by which kamala’s income would exceed Bimala’s income $ = \frac {(14 . 4 – 11)}{11} \times 100 = \frac {3 .4}{11} \times 100 = 30 . 90 \approx 31.$

Correct Answer$: \text{A}$

edited by
Answer:

Related questions

1 votes
1 votes
1 answer
1
go_editor asked Mar 8, 2020
664 views
In a class, $60\%$ of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68\%$ of the students, including $30$ boys, pass an examinati...
1 votes
1 votes
1 answer
2
2 votes
2 votes
1 answer
3
go_editor asked Mar 8, 2020
780 views
If $m$ and $n$ are integers such that $(\sqrt{2})^{19}3^{4}4^{2}9^{m}8^{n}=3^{n}16^{m}(\sqrt[4]{64})$ then $m$ is$-20$$-12$$-24$$-16$
1 votes
1 votes
1 answer
4
go_editor asked Mar 8, 2020
614 views
On selling a pen at $5\%$ loss and a book at $15\%$ gain, Karim gains Rs. $7$. If he sells the pen at $5\%$ gain and the book at $10\%$ gain, he gains Rs. $13$. What is t...
1 votes
1 votes
1 answer
5
go_editor asked Mar 8, 2020
819 views
Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is $5:6$$4:5$$3:4$$2:3$