Question

A man bought an equal number of two kinds of mangoes. One kind 8p each and other at 7p

each. If he had spent his money equally in the two kinds, he would have had 9 mangoes

more. How many of each kind did he buy ?​

Answer 1

Answer:

The answer will be 1008 mangoes in each kind.

Step-by-step explanation:

We have given;

                    Price of mango of one kind = 8p;                                 (i)

                   Price of mango of another kind = 7p;                                 (ii)

  Now, let the no. of mangoes in each kinds be x.

Also, let one mango be A and another be B.

No. of mango A = x;                                 (iii)

No. of mango B = x;                                 (iv)

So, total no. of mangoes = 2x;

Price of mango A = 8 * x;                                 (using eq. (i) and (iii))

                            = 8x p;

Price of mango B = 7 * x;                               (using eq. (ii) and (iv))

                            = 7x p;

Total money spend = 8x + 7x = 15x;

Now, if he had spent half money on each,

the  amount spent on mango A = 15x/2;                               (v)

and, amount spent on mango B = 15x/2;       (vi)      (it's half, according to question)

Now, 8p = 1 mango A;

          1 p = 1/8 mango A;                                    (vii)

Similarly, 7p = 1 mango B;

          1 p = 1/7 mango B;                                    (viii)

Hence, no. of mango A bought in 15x/2 p = 15x/2 * 1/8;              (using (v) and (vii))

                                                                = 15x/16;

no. of mango B  bought in 15x/2 p = 15x/2 * 1/7;                        (using (vi) and (viii))

                                                                = 15x/14;

Now, according to question,

     = no. of mango A bought in half of money + no. of mango B bought in half of money = initial no. of mangoes + 9

                   = 15x/16 + 15x/14 = 2x + 9;

                  = (105x + 120x) / 112 = 2x + 9;

                    = 225x = 224x + 1008;

                   = 225x - 224x = 1008;

                  = x = 1008;

Hence, no. of mangoes A bought by the man = 1008;

no. of mangoes B bought by the man = 1008;

That's all.

Answer 2

Answer:

Man bought 1008 of each kind of mango.

Step-by-step explanation:

Let x be the equal number of mangoes and A be the total amount of money spent

1) for equal number of mangoes:

7x + 8x = A

15x = A

x = A/15

Total number of mangoes = 2x

2)  Equal amount spent on both types, A/2 is spent on each type of mango

quantity of type 1 mango = A/2 ÷ 7 = A/14

quantity of type 2 mango = A/2 ÷ 8 = A/16

A/14 + A/16 = 2x + 9

A/14 + A/16 = 2A/15 + 9

(8A + 7A) / 112 = (2A + 135) / 15

15A / 112 = (2A+135) / 15

225A = 224A + 15120

A = 15120

x = 15120/15 = 1008

So he bought 1008 of each kind of mango.

Check:

When equal mangoes bought, total mangoes = 1008 x 2 = 2016

When equal money spent, 7560 spent on each mango. You get 7560/7 = 1080 of 7p mangoes and 7560/8 = 945 of 8p mangoes.

Total mangoes = 1080+945 = 2025

2025 - 2016 = 9, hence proved