Question

Solve this problem
Sonia wants to purchase a pen. She has money between 200 and 3 300. The cost of the
pen is divisible by 3. If she subtracts *7 from the cost price, she can divide the cost of
the pen by 10 and 20. If she adds 3 to the cost price, the cost price is divisible by 9. How
much will Sonia pay for the pen?​

Answer 1

Answer:

Let the final amount be x.

Numbers divisible by 20 between 300 and 200:

220, 240, 260, 280 ( numbers divisible by 20 are also divisible by 10 )

x-7 = number divisible by 20 and 10

x = (number divisible by 20 and 10) + 7

where, x = number divisible by 3

Numbers so formed:

220+7; 240+7; 260+7; 280+7 (these numbers should be divisible by 3)

Test of divisibility for 3: the sum of the digits should be a multiple of 3

220 + 7 = 227: 2+2+7 = 11 - not divisible by 3

240 + 7 = 247: 2+4+7 = 13 - not divisible by 3

260 + 7 = 267: 2+6+7 = 15 - divisible by 3

280 + 7 = 287: 2+8+7 = 17 - not divisible by 3

Therefore, the only number divisible by 3 is 267.

Thus, x = 267

x+3 = number divisible by 9

267 + 3 = multiple of 9

Test of divisibility for 9: the sum of all digits should be a multiple of 9

270: 2+7+0 = 9 - 9*1 = 9 - divisible by 9

Therefore, the cost of the pen Sonia wants to buy is Rs. 267.

HOPE IT HELPS;)

peace!