# A girl bought a bunch of flowers at the rate of 14 for Rs.180 and sold all of them at the rate of 16 for Rs.220. In this transaction, he gained Rs.50. How many flowers did the bunch contain?

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by nivetangeli

2014-08-30T04:30:33+05:30

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Let us take LCM of 14 and 16. : 112
Let us say she purchased 112 flowers at rate of 14 flowers for Rs 180.
She spent Rs 180 * 112/14 = Rs 1,440

She sold them at 16 for Rs 220.
She gained Rs 220 * 112/16 = Rs 1, 540

She earned profit = Rs 100 for 112 flowers.

If she earned Rs 100 from 112 flowers, she would earn Rs 50 from 56 flowers.

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2014-08-30T13:01:49+05:30
C.P. of 14 flowers = Rs. 180
Therefore, C.P. of 1 flower = Rs.180/14 = Rs. 90/7
S.P. of 16 flowers = Rs.220
Therefore, S.P. of 1 flower = Rs. 220/16 = Rs. 55/4
Gain on 1 flower = Rs. 55/4 - Rs.90/7 = Rs.(385 - 360)/28 = Rs.25/28
Gain       Flowers
Rs.25/28      1
Rs.50          ?
Required number of flowers = (28/25) x 50 = 28 x 2 = 56.
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