The cost of a washing machine is 40% less than the cost of a TV. If the cost of the washing machine increases by 52% and that of the TV decreases by 76%, then what is the percentage change in the total cost of 5 washing machines and 2 TVs?

The correct option is Increase by 0.8%.

Step-by-step explanation:

Step 1: Assume initial costs

Let the initial cost of one TV be T.

Since the cost of a washing machine is 40% less than that of a TV, the initial cost of one washing machine (W) is:

$W=T-0.40T=0.60T$

Step 2: Calculate initial total cost

The total initial cost for 5 washing machines and 2 TVs is given by:

$\text{Initial Total Cost}=5W+2T$

Substituting $W=0.60T$ into the equation:

$\text{Initial Total Cost}=5\left(0.60T\right)+2T=3T+2T=5T$

Step 3: Calculate new individual costs after changes

1. The cost of a washing machine increases by 52%:

$W\text{'}=0.60T\times (1+0.52)=0.60T\times 1.52=0.912T$

2. The cost of a TV decreases by 76%:

$T\text{'}=T\times (1-0.76)=0.24T$

Step 4: Calculate new total cost

The new total cost for 5 washing machines and 2 TVs is:

$\text{New Total Cost}=5W\text{'}+2T\text{'}$

$\text{New Total Cost}=5\left(0.912T\right)+2\left(0.24T\right)=4.56T+0.48T=5.04T$

Step 5: Calculate percentage change

The change in total cost is:

$\text{Change}=\text{New Total Cost}-\text{Initial Total Cost}$

$\text{Change}=5.04T-5.00T=0.04T$

Now, finding the percentage change:

$\text{Percentage Change}=\left(\frac{0.04T}{5.00T}\right)\times 100\%=0.8\%$

Since the result is positive, the total cost increases by 0.8%.