Question

Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?

Answer 1

Let the quantity of apples and bananas purchased be ‘x’ and ‘y’

By the given condition

x + y = 50   ...(1)

Cost of one kg of apple = ${\displaystyle \frac{1800}{x}}$

Cost of one kg of banana = ${\displaystyle \frac{600}{y}}$

By the given condition

One kg of apple = ${\displaystyle 2\frac{\left(600\right)}{y}}$

Total cost of fruits purchased = 1800 + 600

x × 2 ${\displaystyle \frac{\left(600\right)}{y}+y\frac{\left(600\right)}{y}}$ = 2400

${\displaystyle \frac{1200x}{y}}$ = 2400 – 600

${\displaystyle \frac{1200x}{y}}$ = 1800

1200 x = 1800 × y

x = ${\displaystyle \frac{1800x}{1200}=\frac{3y}{2}}$

Substitute the value of x in (1)

${\displaystyle \frac{3y}{2}+y}$ = 50

${\displaystyle \frac{5y}{2}}$ = 50

5y = 100 ⇒ y = ${\displaystyle \frac{100}{5}}$ = 20

x = ${\displaystyle \frac{3y}{2}=\frac{3\times 20}{2}}$

= 30

The quantity of apples = 30 kg

The quantity of bananas = 20 kg