Question

The price of carrots is twice that of potatoes .raj bought 3 kg carrots and 2 kg potatoes for 160.find the per kg price of carrots and potatoes.

Answer 1

Let price of potatoes be x per kg

then price of carrots be 2x per kg

According to question

3 × 2x + 2 × x = 160

6x + 2x = 160

8x= 160

x = 160/8

x=20

therefore price of potatoes = 20

and price of carrots be 2×20= 40

Answer 2

Given,

• The Price of Carrots is twice that of potatoes .
• Raj bought 3 kg carrots and 2 kg potatoes for Rs.160.

To Find,

• Per kg price of Carrots and Potatoes .

Solution :

$\implies$ Suppose the Per kg price of Carrots be a

And, Suppose the Per kg price of Potatoes be b

According to the First Case :

• The Price of Carrots is twice that of potatoes .

$\implies \boxed{\sf{a = 2b}}$   1) Equation

According to the Second Case :

• Raj bought 3 kg carrots and 2 kg potatoes for Rs.160.

$\implies \sf{3a + 2b = 160}$   2)Equation

║From the First Equation Put the Value of a in Second Equation ║

$\implies \sf{3(2b) + 2b = 160}$

$\implies \sf{6b + 2b = 160}$

$\implies \sf{8b = 160}$

$\implies \sf{b = \dfrac{160}{8}}$

$\implies \boxed{\sf{b = 20}}$

║Now Put the Value of b in Second Equation║

$\implies \sf{3a + 2b = 160}$

$\implies \sf{3a + 2(20) = 160}$

$\implies \sf{3a + 40 = 160}$

$\implies \sf{3a = 160 - 40}$

$\implies \sf{3a = 120}$

$\implies \sf{a = \dfrac{120}{3}}$

$\implies \boxed{\sf{a = 40}}$

Therefore,

$\boxed{\bold{\red{Per \ kg \ Price \ of \ Carrots = a = Rs.20}}}$

$\boxed{\bold{\red{Per \ kg \ Price \ of \ Potatoes = b = Rs.40}}}$

$\rule{200}2$