Question

Meena went out for shopping. She had in her handbag approximately Rs. 15/- in one rupee notes and 20p. coins. When she returned she had as many one rupee notes. She actually came back with one-third of what she had started out with.
How much did she spend and exactly how much did she have with her when she started out ?

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Answer 1

Meena spent Rs9.60 and she had Rs14.40 when she started out.

Given: Meena had Rs15 in one rupee note and 20paise coins. She came back with 1/3rd of what she started with.

To Find: Money she spent and money she had when she started out

Solution:

Let, Meena had in rupees = a

Meena had 20p coins = b

So, she started out with (100a+20b) paise

She came back with (20a+100b) paise

According to the question, she returned with 1/3rd of what she started out

So, (20a+100b) = $\frac{(100a+20b)}{3}$

By performing cross-multiplication,

3(20a+100b) = (100a+20b)

60a+300b = 100a+20b

300b-20b = 100a-60a

280b = 40a

$a = \frac{280}{40}$

a = 7b

Let us assume that b=2

Then, a =  7*2

a = 14 (This is near to the approx value given i.e., 15)

Therefore, Meena went out with Rs14.40

Meena came back with 1/3rd of it so,

$\frac{14.40}{3} = 4.80$

Amount Meena spent = 14.40-4.80

Meena spent Rs9.60

Answer 2

Meena spent Rs9.60 and she had Rs14.40 exactly when she started out.

Given,

Meena had Rs15 in one rupee note and 20paise coins. She came back with 1/3rd of what she started with.

To Find:

Money she spent and money she had when she started out

Solution:

Let us assume that originally meena had X rupees and Y 20 paise coins. Going shopping she had (100X + 20 Y) paise.

She returned with only (100Y + 20X) paise.

This last some as we know is one third of the original and therefore

3(100Y+20X)= 100X + 20Y

Simplifying we have X=7Y

If Y=1 then X=7. Assuming this so Mina had 7.20 rupees when she set out for shopping

This is wrong because Meena actually had about 15 rupees.

Let us see now what we get if Y=2. Then X=14.

The original sum was 14.40 rupees which accords with the condition of the problem

If we assume that Y-3 then the sum will be too big - 21.60 rupees.

Therefore the only suitable answer is 14.40 rupees.

After shopping Meena had 2 one rupee notes and 14 twenty paise coins.

This is actually one third of the original sum 1,440:3 = 480

Menace purchase therefore, cost

14.40 4.80 = Rs. 9.60

Hence, Meena spent Rs9.60 and she had Rs14.40 exactly when she started out.

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