Question

The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?
A.3:4
B.2:3
C.1:3
D.2:1

Answer 1

Given:

(i) The number of oranges in three basket are in the ratio 3 : 4 : 5.

To find:

(i) In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3

Solution:

For the first case, given the ratio of oranges in the 3 baskets is 3:4:5.

Let the common ratio be x.

So,

1st basket has 3x oranges.

2nd basket has 4x oranges.

3rd basket has 5x oranges.

For the second case, the ratio of oranges in the three baskets become 5:4:3. Let the common ratio be y.

So,

1st basket will have 5y oranges.

2nd basket will have 4y oranges.

3rd basket will have 3y oranges.

Given that the increase in oranges takes place in the first two baskets only so the number of oranges in the third basket remains constant.

As a result,

No. of oranges in 3rd basket initially = No. of oranges in 3rd basket finally

⇒ 5x = 3y

⇒ x = 3y/5

Now, let us replace the value of x in the first case as x = 3y/5.

So,

3x : 4x : 5x

= 3(3y/5) : 4(3y/5) : 5(3y/5)

= 9y : 12y : 15y  ...(1)

The second case has a ratio of 5y : 4y : 3y

Multiplying this with 5, so as to compare this with (1), we get,

5 * (5y : 4y : 3y)

= 25y : 20y : 15y

On comparing this with (1),

We see 9y has increased from first case to 25y in the second case.

So, net increase in first basket = (25-9)y = 16y

Again, 12y has increased from first case to 20y in the second case.

So, net increase in second basket = (20-12)y = 8y

Thus the required ratio becomes 16y : 8y

= 2:1.

Thus, the ratio is 2:1, and (D) is the correct alternative.

Answer 2

Given :

The number of oranges in three basket are in the ratio 3 : 4 : 5

The new ratio of number of oranges in three basket = 5 : 4 : 3

To Find :

The ratio in which number of oranges in first two basket increased

Solution :

Let The increased number of orange in basket 1 = x

Let The increased number of orange in basket 2 = y

The number of oranges in three basket = $B_1:B_2:B_3$  =  3 m : 4 m : 5 m

And

New ratio of number of orange in three basket = $B_1:B_2:B_3$ = 5 n : 4 n : 3 n

∵  Number of oranges in third basket remains same

So,   5 m = 3 n

Or,    

So,  $B_1:B_2:B_3$  =  3 ×$\dfrac{3n}{5}$  : 4  ×$\dfrac{3n}{5}$ : 5 ×$\dfrac{3n}{5}$

                           = $\dfrac{9n}{5}$ : $\dfrac{12n}{5}$ : $\dfrac{15n}{5}$

∵    The increased number of orange in basket 1 = x

And The increased number of orange in basket 2 = y

So,  $\dfrac{9n+x}{5}$ : $\dfrac{12n+y}{5}$ : $\dfrac{15n}{5}$ = 5 n : 4 n : 3 n

Or,  $\dfrac{9n+x}{5}$ = 5 n

i.e 9 n + x = 5 n × 5

Or, 9 n + x = 25 n

Or,   x = 25 n - 9 n

∴     x = 16 n

Similarly

$\dfrac{12n+y}{5}$  = 4 n

i.e 12 n + y = 4 n × 5

Or, 12 n + y = 20 n

Or,   y = 20 n - 12 n

∴     y = 8 n

So,

The increased number of orange in basket 1 = x = 16 n

And The increased number of orange in basket 2 = y = 8 n

∴  The ratio of number of oranges in first two basket = 16 n : 8 n

                                                                                       = $\dfrac{16n}{8n}$

                                                                                       = $\dfrac{2}{1}$

Hence, The ratio of number of oranges in first two basket is     2 : 1   Answer