Question

Ram bought ‘a’ flowers for ‘b’ rupees, where ‘a’ and ‘b’ are integers. If he had bought
10 more flowers he would have got all for Rs. 2 and saved 80 paisa a dozen. What are the respective vales of ‘a’ and ‘b’?
1. 5,1
2. 4,2
3. 3,2
4. 6,1

Answer 1

Answer:

5,1

Step-by-step explanation:

Answer 2

The Value Of A Is 5 And B Is 1

GIVEN

Number of flowers bought = a

Cost of the flowers = b.

a and b are integers.

TO FIND

The value of a and b.

SOLUTION

We can simply solve the above problem as follows-

It is given -

Cost of 'a' flowers = Rs b

cost of a+10 flowers = 2 Rs. ( 200 paise)

Cost of one flower = 200/a+10 (equation 1)

So, b>2

We know that the value of an integer can be zero and decimals

So,

b = 1 Rs (100 paise)

So,

Price of 1 flower = 100/a (equation 2)

Amount of money saved per 12 flowers = 80 paise.

Amount of money saved on 1 flower = 80/12 (equation 3)

From equations (I), (ii), and (iii)

$\frac{100}{a} - \frac{200}{a + 10} = \frac{80}{12}$

$\frac{a + 10.100 - 200.a}{a.a + 10} = \frac{80}{12}$

$\frac{100a + 1000 - 200a}{ {a}^{2} + 10a } = \frac{80}{12}$

$\frac{1000 - 100a}{ {a}^{2} + 10a } = \frac{20}{3}$

$3000 - 300a = 20 {a}^{2} + 200a$

$- 20 {a}^{2} - 500a + 3000 = 0$

$- 20( {a}^{2} + 25a - 150 ) = 0$

Dividing LHS and RHS by -20

${a}^{2} + 25a - 150 = 0$

${ a }^{2} - 5a + 30a - 150 = 0$

$a(a - 5) + a(a + 30) = 0$

(a-5) (a+30 ) = 0

a = 5

a = -30

Hence, the value of a is 5 and b is 1

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