Question

An amount of Rs. 2430 is divided among A, B and C such that if their shares are reduced by Rs. 5, Rs. 10 and Rs. 15 respectively, the remainders shall be in the ratio of $3:4:5$ . Then B’s share was?

(a) Rs. 605

(b) Rs. 790

(c) Rs. 800

(d) Rs. 810

Answer 1

Hint: We will assume the original price to be some variable ‘x’. Here, we have to find B’s share before reducing the price. So, we will get that by using the formula $\left( \text{remainder}\cdot \text{original price+reduced price} \right)$ . By using this we will get B’s share as $\left( 4x+10 \right)$ .  Similarly, we will find for A and C. Now, for finding value of x, we will add all the shares of A, B and C and equate it with total amount given to us i.e. Rs. 2430. Thus, we will get the value of x and will put in $\left( 4x+10 \right)$ to get an answer. 

Complete step by step solution:

Here, we have to find the original share of B before reduction of price. So, we will assume the original price to be let’s say ‘x’. So, the share of A, B, C before reduction can be written as $\left( \text{remainder}\cdot \text{original price+reduced price} \right)$ . 

So for A, we have the ratio as 3 and the reduction in share as Rs. 5, therefore we can write the share of A as (3x+5).

Now for B, we have the ratio as 4 and the reduction in share as Rs. 10, therefore we can write the share of B as (4x+10).

Lastly, for C, we have the ratio as 5 and the reduction in share as Rs. 15, therefore we can write the share of C as (5x+15).

So, we get  $\left( 3x+5 \right),\left( 4x+10 \right),\left( 5x+15 \right)$ respectively. Now, the total amount is given as Rs. 2430. So, we will add all the shares and equate it with the total amount. We will get as

$3x+5+4x+10+5x+15=2430$   

On further solving, we will get

$12x+30=2430$  

$12x=2430-30=2400$  

On dividing 12 both sides, we will get as

$x=\dfrac{2400}{12}=200$    

So, now we have to find B’s share only. So, we will substitute the value of x in $\left( 4x+10 \right)$ , we will get as

$\left( 4\cdot 200+10 \right)=Rs.810$   

Thus, B’s share is Rs. 810.

Hence, option (d) is the correct answer. 

Note:  Another approach to solve this problem is by subtracting reduced price from the total amount given i.e. $2430-\left( 5+10+15 \right)=Rs.2400$ . So, now we can find B’s share by multiplying it with remainder upon total ratio i.e. $\dfrac{4}{3+4+5}=\dfrac{4}{12}$ . On using this, we will get as $2400\times \dfrac{4}{12}=Rs.800$ . Now, students make the mistake here that they do not add Rs.10 which we previously deducted from the total amount and consider Rs. 800 as the final answer which is wrong. So, we have to add Rs. 10 to get the final answer as Rs. 810.